I only have 3 spots in my stable.
They currently have:
DLC War
DLC thoroughbred
Mustang Wild Bay
I picked up a Mustang Grullo Dun and wanted to keep the 4th.
I'm normally running around hunting with 2 horses, main and temporary but I can't keep the temp horse or store it in the stable.
I recently found the Arabian White, super nice horse, so I sold my Mustang Grullo Dun.
I kinda thought the idea was to brake horses or steal them, then keep them for a while so you get better skills with them, then turn them in for more money. It's hard to do that when you don't have the room to work with in your stable. I wish there was an option to take them out and put them back at a later date if I wanted.
I found a nice Nokota but don't have the space to work with it. Same went for a nice looking Hungarian Halfbred.