I think that a .357 with appropriate load would be adequate in killing a deer. Shot placement and range is needs to be held at the highest importance. 50 yards, shot to the head or heart should kill one pretty well. Sure it probably has a better effective range than 100 yards, but if I were hunting with a .357 I would feel better about taking the shot the closer the deer would get to me.
.223 is adequate, not the best and not the worse option. Shot placement and bullet choice is just as important as with the .357. I would prefer to go after younger/smaller deer with a .223 than I would if I were hunting for a trophy buck. In the state of Georgia, it is technically legal to hunt deer with a cartridge as small as .22 hornet, although that is not really ethical.
The woods are thick here, and the deer tend to appear out of the brush 50 yards or less away. Marlin 336 in .30-30 or .35 Remington make great deer rifles.