'Don't know where you are hunting and how big the deer are or what kind of deer ... Whitetail? Muley? That will probably do the job, but the risk, IMHO, is sticking to the ground rules you set for yourself.
I was hunting in NW FL a few years back with a Blackhawk .357 w/open sights. I intended to limit myself to little more than the same range I had successfully archery hunted (30-35 yds), just to be on the safe side. A perfect silhouette shot came my way, I said to self, "That's just a tad over the planned range ... looks like about 45-50 yds ... maybe
. I held high on the shoulder and shot and he took off like a rocket. I hung my head and started cussing. Then I heard a crash about 30-35 yds beyond
where he had stood in a small dense creek bed. I walked down there and found him. Stone dead. I could see where he had run about 40 yds, circled around in a 180 and veered down into the creek bottom, and headed in the opposite direction he was facing when shot. He went another 50-60 yards in that thick bottom before expiring. He actually ran a total of about 120-140 yards from the point of impact until he lay down for good. In some circumstances, that's enough to lose the trail on a wounded deer. And it darned sure ain't "dropped dead where he stood", if you know what I mean.
Once it was all said and done, I had to own up to having taken the shot at nearly 70 yards! That buck fever does wonders for the old eye sight autoranging function, huh? Then I realized my store bought Remington Corlokt 158 gr semi jacketed bullet had centerpunched him, but it had gone in one side between two ribs and out the other side between two ribs. Never recovered the bullet, but I could just about get a ballpoint pen in the exit wound.
The bullet never even opened up. Never found a fragment, but it did manage to do the deed on the rear of the lungs as it traversed through the little buck. A small 6 point "swamp buck", we called them. I was lucky.
So, tale told, I never took a .357 hunting deer again. Even though it did it's job, I couldn't trust me to do my part. I have never lost a shot deer to this day but I danged near lost that one. If I ever do take it out to hunt again, it will be with some fare-thee-well loads from my bench off the Dillon. But now I have a SBH w/10in barrel in .44 Mag for that.
If you can keep your range down and know where your bullet will impact, go ahead. But I can tell you from that one experience, that's a tall order under the exitement of the hunt. I still get that way, thank God.