I am a little unclear about what you are asking. Are you wondering about being selfish about moving out, or about expecting your Dad to look after your horses?
It isn't unreasonable to want to move out at 22, as you are now an adult. Moving out because you and your mom don't get along is another issue altogether. In my mind, the difference between the two also means the difference between whether it is reasonable for your dad to help out and care of your horses. I am going to be blunt because I don't know how else to put this. Please don't take offence as none is intended. So there are two possible scenarios (and these are extremes to make the point)
The child-like and "selfish" response would be to move out to spite your mom, or to move out because you won't / can't find some middle ground with her. Expecting your dad to keep and look after your horses because you and your mom cannot see eye to eye is also selfish. Once you commit to moving out because you want to exercise your roll as an adult, you also take along with that the responsibility of caring for your animals or making mutually agreed upon arrangements.
The adult thing to do is to recognize why you are moving and take ownership for it. As part of that process, you acknowledge your mom as another adult and accept that she can hold different views, and then find a way to make your decision to move out a genuinely happy occasion for both of you. You want to move out when you are on good terms with your parents, and you want them to feel proud of you for becoming the wonderful adult they hoped to raise. Again, the horses. The adult response is to ASK if (both) your parents are willing to continue caring for your horses and find out how you can contribute either financially or physically. They do not owe you this, so you are asking and preparing yourself in the event that you have to make other arrangements. I think most parents would want to help out their kids and so they would be amicable to some arrangement. Whether they want you to contribute or not is beside the point. Asking is the point as it shows that you respect them rather than take them for granted.
I assumed your mom and dad live together, but this was a little unclear in your post. Please forgive me if I have assumed incorrectly.
I hope this helps shed a little perspective.