We always use 55g ballistic tips out of 222, 223, 22-250, and220 swift. All of them have killed forked horn mule deer very well. We shoot them in the shoulders to drop them, usually have to follow up on a 2nd shot when you get there. If you hit them behidn the shoulder, they'll run a little ways, but the blood trail wont be very big, so it better be an open spot to where you can see it going. Theres no problem in using .22's for deer, just be smart with your shots.
That's all I used to use in Montana before I "knew better". I used 50 grain Speer spitzers and IMR4198. Never had a bullet go clear thru but most of the time the bullet was under the hide on the far side. When I got my .223 I used the old Nosler 555 grain solid base boattails and they worked very well also.