If it's all you have to hunt deer with, then by all means use it.

As far as recoil goes, I stilll consider the .338 Win the heaviest recoiler in my battery. But it's quite a bit lighter than the .375 H&H next to it. Rifle weight makes a difference. I don't shoot 3-1\2"slugs so can't speak to that, but 3" slugs don't earn my attention like a .338 with 250-gr bullets will.

I much prefer something lighter for deer. But, being one of those who's hunted elk with a .243 because it was all I had, that works the other way, too. I consider it far too heavy for deer, but if it's all you have, use it.