All though several will disagree, I believe the .357 fired from a rifle is quite suitable for deer, at ranges where the shooter can guarantee a proper hit, AND, with the right bullet for the job.
Firing out of a rifle length barrel drives the bullets much faster than from a handgun. Bullets designed to expand at handgun speeds usually expand violently (like varmint bullets) at rifle speeds, and lose a large amount of their penetration.
SO, don't go with the 125gr JHP, or similar type ammo. Choose a heavy (for the caliber) bullet like a 158gr, or a 180 if your gun will shoot them well enough. Hard cast bullets and soft points work better on big game than light hollowpoints out of a rifle.
Keep the range short (for a rifle), pick your shots (and with the H&R, you only get one!) and bring home the venison.
Its not a good 200yd plus cartridge, and many would only go half that, to ensure a humane kill. It is more dependent on your skill with the rifle and ammo you choose, where the upper limit of your effective range is.
Basically our of a carbine the .357Mag, with the proper ammo for the job is a little bit less powerful than a .30-30. Not enough for the deer to notice, if you hit them right, but enough to make hitting them, and what the right place is, a more limited choice.
At over 100yds, I wouldn't take a shot that meant going through the shoulder (or any other heavy) bones. Neck or broadside through the ribs would be ok. Long quartering shots are iffy. If I'm not CERTAIN I can get the hit I want (and need), I won't shoot. The .357 has enough (within its limitations) for deer, but it doesn't have a lot of extra left over, so using it within its limits for humane kills is vital.
Lots of people these days don't think the .357 is enough for deer (or at least lots of people posting on the net think that), preferring to use something else, with a larger envelope of limitations. The .357 Mag can work, and will work, but you have to do more to make it work right than you do with a full size rifle round.
Since you are looking at deer with a single shot rifle, you might want to consider a larger round, if there are not any other significant considerations. Of course, the bigger the cartridge, the more the recoil, something that can be very noticable in a light single shot rifle. On the other hand, you only shoot it once, at a time....