Well i finished Promises to keep,and yet louis ran away without mounting Frost.I see no reasons why i shouldn't take him point is,if i dismount,where it will be located next time i need him?

I think he stays where you leave him. So preferably in a stable But he will show up as soon as you fast travel.

mhmm actually i fast traveled to whiterun to set him here but he disappears if i go away.Furthermore,stealing him in whiterun gives 50 bounty in Falkreath O_O any tip how can i just place him somewhere and how?I never bought nor used a horse.

Honestly? If you have a hard save shortly before you got the horse, I'd reload it and redo the quest and select the option to keep the horse, otherwise you're going to get tagged for stealing him every time you dismount and remount.

Frost is my favorite horse, so if you're only backtracking about an hour or so, it's so worth it.

Ah, you stole him. Then he will go away when you dismount.

I found him mostly annoying, actually. Too bad you can't sell horses...