So when i fast travel the horse will be in the stables but what is i used carriage and left my horse in another city???
Will the horse be in the stables again?? Or will he be left out from the town/city I came??

If you own a horse then whenever you fast travel he will be there. You could travel anywhere on the map using fast travel and whether its near a city or in the middle of no-where your horse will be next to you when you spawn.

I don't use fast travel for RP purposes, if i use carriage will it be the same?

Go to a stable to see if your horse is there. Save the game. Use a carrriage to go to a different city and then check see if your horse is next to you or at the stable. If he is or isn't you'll know the answer and be able to reload the game so it doesn't affect your RP.