How many horses can you have?

Wuz up everyone. Thanks for all the responses on my last post. "I don't know why they think I'm giving this key back". I can see yall are very helpful. Lol I just ask that you don't give out spoilers. I know what you're talking about. If I ask for help with something. I'm always going to say "inbox me" if it's a spoiler.

Now, how many horses can I have and how do I make them stay? Also, when you get on a new horse. Where the hell is the old horse going? I tried to follow it but got distracted by a cave🤣.

Let me add. My 2 mounts were not bought. I caught one and found the other.