You can own more than one, but you will probably need the UFO overhaul to have companions ride your other horses. You can install a whistle spell to call upon your horse, but downloading a mod that allows your horse to be a follower will make your horse follow you just like a companion.

theres a mod on workshop that summons your horse you last rode

thank you, Ill have a look tomorow, night

this is what i did i baught the dragon bone horse there in Solitude and once i got Frost and Shadowmere i went back to solitude got off either of them and then hopped on the dragon bone horse i owned Shadowmere and Frost are designed to stay in the location you last rode them before mounting another owend horse ... so both shadow and frost are sittin in solitude where i left them when i mounted the dragon bone horse you see? all purchased horses return to the stall in which they were baught so you can own all of them and ride all of them but if you must leave frost and shadowmere in the same location or youll loose them in the world. i once lost frost and while riding the dwarven horse i found frost got on him FTd to Solitude jumped off him and rode the Dragonbone horse to markarth and jumped on the dwarven horse. the dragon bone horse went back to solitude as they are designed to do. i know this because when i went back to solitude with the dwarven horse all three were standing there shadow frost and the dragonbone... when you travel to eatch stall youll see your horses. this mod is flawless cept for human error and the small glitch in which shadow doest get his armor simple fix reload the mods and then fast travel with shadowmere and he will have his armor.

Cant find that ♥♥♥♥♥'a in Windhelm ;-;