I think that the .357 would be fine if used within it's limitations (50ish yards max). However if I were shooting beyond 30 yards, I would not want to have to count on bullet expansion. I would use a nice, heavy LFN or SWC (I like the 358429-173 grn SWC). I am always concerned about boolit placement and penetration. If you have those two, then the deer will be yours.
I hunt with a Ruger Blackhawk in .45 Colt (scoped) or in .41 Mag (open sights). Depending on the range and conditions that are expected for that day.
Regardless of which gun I use, I use heavy, cast boolits. I'm very happy with the results they deliver.
I don't use a .357 only because my longest bbl revolver in .357 is 3 3/4". If I had a nice, 6" accurate gun, it would be fine for the areas I hunt. (Max range us usually 35 yards or so).
All that being said; pick a good, heavy, accurate boolit/load combo and practice, practice, practice.
Remember, whether you are talking about hunting or self defense, the priorities are the same:
Shot placement is king; penetration is queen; everything else is just angels dancing on the head of a pin.