Match the gun to the game, and be sure to check your local game laws.
Yes, a .357 Mag will work with deer and similar size critters. Especially for the smaller deer like in the Texas hill country. Be sure to load it with proper HUNTING ammo.
Also, a .357 Mag revolver can work really well for small game, just load it up with light .38 Spls, like wadcutters. Again, be sure to check your local game laws. I know that this is NOT legal to do in Georgia. At least it was as of last year. Idiotic, but true.