Ride Odahviing

I couldn't wait in the room with Odahviing because of "nearby enemies", so in my attempt to make the Jarl leave, I went to another zone, waited there, and returned. Afterwards, I was able to wait in the room with Odahviing. This also resulted in not everyone immediately attacking him once he was free, which solved my problem.

I think it must have been a glitch that never cleared Odahviing as an enemy when he was captured. If this happens for anyone else, try zoning back and forth to see if it is solved.

Frost only becomes your horse if you persuade Louis Letrush to let you keep him or kill after you talk to him after you have stolen Frost from the Black-Briar Manor. If you just ride off without completing the quest Frost will just return to where you first stole him (Black-Briar Manor).

If you own him and you were to mount another horse (at least another horse you own) he will remain at the location you left him so far as I can tell. I use Shadowmere (who seems to do the same thing) and I just parked Frost at a stable so at least he would be safe. He has stayed there since.

Also any horse you bought from a stable will return to that stable when you begin using another horse. When I first got Shadowmere the horse I purchased from Whiterun began to walk away and when I next went back to the Whiterun stables he was there safe and sound.