Welcome to the Forum from North Texas! We're mighty glad you decided to join us! You shouldn't have too much trouble hunting deer with a .357 revolver. You should use heavy loaded magnum rounds. If you can find some loaded with Keith bullets (semi-wadcutters), you should be good to go! Be sure to practice at ranges out to 50 yards. If you reload, you should be able to develop the perfect deer load.
I've deer hunted with a .44 Mag but have friends who have hunted deer with a .357 using cast Keith bullets backed with a stiff load of 2400 with great success (read: they brought home the venison). I don't recall the load, but it was safe for a Smith and Wesson revolver.