After skinning the animal, you can load the carcass to your horse and bring it back to a trapper or butcher to sell it or back to the camp where you can donate it for provisions. If you intend in selling or donating the animal’s carcass, it’s better to stow it unskinned first then carry it to the butcher or back to camp. You can then skin it before selling/donating it.
Here’s what your horse can carry:
Carcasses:
Pelts/Skins:
How to increase your horse carrying capacity
You can double the amount of your horse carrying capacity by bringing another horse. Since you can only get one of your stabled horses at a time, the only chances that you’ll get another horse are by getting someone else's or breaking one from the wild. You can load the same number of animals and pelts in the other horse. Only one of these horses can have your saddle (with your weapons and other cargo are stored) so the other horse will only serve as a mule.
If you enter a stable with an extra horse loaded with carcasses and pelts, you'll have to either stable that extra horse or sell it. The carcasses and pelts it is carrying will be dumped outside the stable for you to recover.