Why would you want a sex toy replica? You can use it to desensitize/stretch yourself before doing the deed, to have confidence you can take the animal's size at all or train yourself, or perhaps you just like animals and looking at their tools between sexual activities. I can tell you the real replicas are awesome compared to most online toys which are generally abstract animal-like shapes. The materials will cost about as much as 1 toy from a toy artist and most of it is reusable. You can modify the hardness or colors of the final product however you want. You can start soft/squishy for a huge animal you're not ready for yet and up the firmness as you train yourself. The softer toys will gently push against you to retain their shape but will squish a bit to get past your hole. It's easy to keep making toys once you've done it. The safest toys are made from platinum-cure silicone, and that's just mixing part A to part B and pouring into a mold. A bit later and your toy is ready.
You will need:
A cardboard box (larger is better).
An unscented wax candle
Scissors or box cutters
A large and deep pot and a stove and oven
Hot glue gun + glue ammo (sticks)
Fast-set alginate mold making powder
Water and measuring cups
Platinum cure silicone 10A or 20A or 30A hardness (you can also buy on smooth-on.com)
A few containers and things to mix with
Things will be easier and product will look better if you also get:
Gram-accurate kitchen scale
A silicone spatula / scraper
Silicone color pigments
A vacuum chamber and vacuum pump (highly recommended if you can spare the money but not necessary)Edit
Plan out the hardness and color of the product that you want. Silicone is measured by a number called shore hardness. The materials useful for this project range from 10A to 30A. 10A will let the shaft stand upright but be fairly jiggly and any challenging parts will squish under pressure but always push somewhat gently to keep their original shape. 30A is hard but still has some give to make it comfortable; the dimensions will be almost entirely static as you use the toy. Also the harder it is the more the surface feature of the animal penis will give the toy a rough feel (veins, ridges, etc). Some prefer it that way. When you get more advanced you can dual-cast your toy with silcones of two different hardnesses. The surface can be softer and the core can be harder, so it retains its dimensions under pressure but feels smoother. That step isn't covered here but I think there's enough info to give a good enough idea of what that entails.
Measure your animal penis when he's fully erect. Take all three dimensions (length, width, and height). If you want to save costs you will want to take a measurement of all major features of the animal penis to get as close-fitting a mold as possible. For a dog that would mean W+L+H for the shaft and knot. I've never done a horse but I imagine that's shaft + flare. Take multiple measurements and average them out. Your animal will shrink a bit as you fiddle with measuring tools so a few gentle tugs in the right place before measuring is a good idea. I like to use digital calipers that I see on eBay for about $7 but that's not needed. Before using them I sand down or cover any sharp edges. Add at least .25 inch clearance to all measurements.
Cut cardboard pieces to make a cardboard container to hold mold making liquid in. This will end up functioning similarly to an artificial vagina for animal breeding. The easiest way is to just make a box from cardboard pieces that is bigger than the fully erect penis. To save money and material, for a dog you can cut pieces for a rectangular box for the mold and shaft separately. This will make the mold fit better and save on material.
Dip the cardboard pieces in wax to prevent the water from making them soggy. Alginate oozes water over time which messes with cardboard. Fill a large pot with water and set it to boil. Get a large disposable container (plastic is fine) and put your candle in it after removing any stickers and such then place the container in the boiling water. It'll take a while to melt. Once it's fully liquified you can turn off the stove and remove the container with wax. Dip your box pieces into the wax using some tool to avoid burning your hand. Raise the piece above the wax to let excess wax drip off. It's okay if you need to bend the piece to get it into the wax container - just straighten any pieces out before the wax hardens.
Use your hot glue gun to glue the pieces together. Try to make it as water tight as possible, and check the seams a few times for any gaps in your line of glue. Don't test the water tightness though.
Prepare what you need to make a mold in advance of bringing in your animal. Everything needs to be planned out. You'll need a large container filled with a measured amount of water, a bag of alginate powder, a completely rigid mixing stick or spoon, and your cardboard mold container. Filtered water works best and well-water may not work at all. If you're using the linked materials, you can use 6.5 cups of water to 1 bag of alginate. Using the gram kitchen scale for accuracy is a good idea. You want fast-set alginate powder so it hardens before any animal jizz messes up the mold too much. After it hardens more jizz doesn't matter much. That's why I linked alginate that hardens in roughly 2 minutes.
Get your animal hard and as aroused as possible, then very quickly make the mold. The best method to do that depends on your experience with your animal. Handjobs might work. A full breeding and pullout might work. If it's a dog you can keep the knot outside and use your hand to keep pressure behind the knot while you get bred. You can let him mount you and use a completely flexible and well-lubed sex toy like a pocket pussy. Spend 2-5 minutes jerking him off. Most semen comes out in the beginning and it's best to deplete him as much as possible. When that's accomplished, quickly mix your powder and water in a container. You need to move fast before it hardens - fast enough that you're almost spilling material everywhere. Pour the alginate mixture into your cardboard mold container. Give a few tugs on your animal's penis in the right places to get him as large as possible because he'll shrink somewhat as you mix the powder. Then immediately put the penis into the alginate liquid and hold the mold container in place. Put some spare alginate mixture on top to ensure everything is covered evenly. Hold it in place until your animal goes soft and can be removed from the mold. The alginate can deform under pressure so you don't want to have the mold hanging from him or tug on the mold to try to pop him out quicker. Try to prevent your animal from eating any spilled alginate.
You need to prepare and pour silicone into the mold as soon as possible. The alginate will start to dry out and deform as time goes on. Estimate how much silicone you need. 2 cups will generally do it for a 150 lb dog and smaller. You can also pour water into your mold and check the volume of the water using measuring cups. You should rinse out the mold anyway from detatched bits of alginate and animal jizz. Add 1/4 cup more than what you expect to need. Follow the directions for the silicone and pour into a container. If your going to follow the optional Vacuum Degassing step then you can pour directly into the vacuum chamber pot. For Smooth-On Dragon Skin Silicone, you pre-stir part A and B to even out the mixture that might have settled a bit at the bottom during shipping and then mix equal parts A to B in your mixing container. Mix it slowly but thoroughly. You're now on the clock and need to finish preparing the silicone before the "pot life" expires (before it starts to harden) that is listed in the instructions. You want to make as few air bubbles as possible but air bubbles will happen regardless. Make sure to scrape the side of the mixing container and the bottom. If you want to add any colors mix it in now. The pigments are highly concentrated so you generally only need a drop or so but add to suit your tastes. At this point if you have a vacuum chamber and vacuum pump, use it to remove air bubble that will always be in the silicone by this point even if you can't see it. See Optional Degassing Step for details. Pour the silicone into the alginate mold slowly using a thin stream of silicone. Try to let as much fall naturally as possible. By the end you probably will need to gently use your silicone scraper tool to push the remaining silicone into the mold (air bubbles can appear this way). Once the mold is filled, cover it in a plastic bag and remove as much air as possible before you tie the top. Wait the time listed on the silicone instructions (varies by hardness of the silicone) without disturbing it. Clean silicone off of your silicone spatula because it will bond to it if it hardens. Alginate is also easier to clean off of things before it dries.
Adding a base. You may have noticed that your dog's mold does not include a base for the toy that will make it safe for insertion into your body. You cannot insert a toy without a large and reliable base to prevent it from disappearing inside of you. If that happens, an ER doctor will likely have to remove it and judge your craftsmanship (hopefully complements). To add a base you need to make a prototype using one of various methods. For example, you can use sculpey oven-bake clay to make it by hand or 3d print it. Any reasonably hard and water-resistance material can be used. When you have your prototype base ready, repeat the previous steps but use the prototype instead of your animal. Once you have a silicone replica of the base, you can mix a bit of silicone and use it like paste to bond it to the toy. Find some way to hold the base and the toy in place while the silicone hardens.
After the time is expired you can remove the now hardened toy. The alginate is one-time use so you will need to tear that apart but you can use the mold container multiple times if you want. The alginate will pop out of the mold container in 1 piece. You will probably need to pull / cut off small bits of excess silicone. Air bubbles in the mold will create teeny bumps which are no big deal and pull off easily. You can mix a bit of silicone and use it to cover and smooth over any sharp parts left over by cutting excess silicone off. It is recommended that you post-cure your toy. Even though it is hardened and in my opinion usable, the material will be the strongest and last the longest if you do this. Follow the instructions that came with the silicone that will vary by hardness. It will involve baking it to a specific temperature for a period of time and then letting it cool.
Optional Degassing Step:
No matter what you do bubbles will appear as you mix and pour the silicone. Vacuum degassing is like a pressure cooker but in reverse. It sucks out all the air. When the pressure drops it causes the air bubbles inside the silicone to expand and try to push out of it making it look like it's boiling. Ideally you'll get a vacuum chamber that is big enough to be at least 2/3 bigger than the amount of silicone you're using. Cover the vacuum chamber pot. Close the valve that lets air into the chamber and open then valve that goes to your pump. Check the level of the vacuum oil and fill if needed. Turn the pump on. As the pressure drops the silicone will bubble and rise. You can shake the vacuum chamber back and forth like a paint mixer to help the air escape. Monitor the level to ensure it never gets within .5 inches of the top. If it gets too close open the valve that lets air into the chamber a little bit and then close it. The silicone will rise spectacularly and then collapse and then kind of gently bubble for a while. Let it degass for 5 minutes or so. Chances are your vacuum chamber won't reach the sucking power recommended by the directions but that's OK if its close. After it's done, close the valve that goes to the pump and turn the pump off. Slowly open the valve to let air back inside the chamber. It needs to be slow because it will blast air back into the silicone otherwise. Then open the value to your pump. The silicone is now ready to pour into the mold.