My opinion is the the 357 mag is marginal for hunting whitetail deer. It will kill them with a good hit.
My first centerfire revolver was a 6" Colt Python (357) which was bought for deer hunting, home defense, and range time. About that time I was doing a lot of reading in the gun rags about handgun hunting. Decieded that the 357 mag was a tad light and was better off with a 41 or 44 mag. Never really considered a 45 Colt at the time, but factory loads then were very wimpy.
Got a 41 mag to use deer hunting. Never shot a deer with the 41 mag, but I was confident that it was just fine. I later bought a SRH in 480 Ruger and it became my deer hunting revolver since I did not want to drill and tap my M57 for a scope.