Wild Horse locations after I tame them?

Hi, so I’ve been taming the wild horses in the new AE add on, and I was wondering where the horses went once they were tamed. I tamed one, registered it at the stable, then went to tame another and repeated the process. Where did the first horse go? Whenever I fast travel it’s only the most recently tamed horse. Can I only permanently tame one? Thanks in advance!