How do you get your horse out of the city of Bruma?

Are you having the "Bruma is hiding my horse" glitch? Just fast-travel to somewhere outside (a stable, an inn, etc) and your horse should appear next to you.

I do that but my horse stays in Bruma but only I travel. I also did the "MOVETOQT" cheat but I always end up in a house or something with my horse.

You could try clicking on your horse in the console, then going somewhere outside of a city and typing "moveto player" into the console, without the quotations, of course. Unless I'm not fully understanding what is going on this should warp your horse right next to you.