It can be done. I've shot enough muledeer with a 44 to decide that 50 yds is about as far as I'ld care to whack an elk with a 250 gr keith cast bullet from a 44 magnum.
Still hunt the timber in an area with limited tags and you won't be at much of a disadvantage. But to go into a general license area with a handgun as your only option is probably going to about triple the chance you will be in the 60% unsuccessfulhunters group.