Funny thing, I just just shot a mule deer with a 22-250 yesterday. My undoubted conclusion is it's absolutely enough gun.
I only used a 50 grain ballistic tip. It worked exactly as one could hope. There wasnt much left of the heart and lungs. It also gave me an entrance and an exit hole.
As with any caliber you just have to know its capabilities. No need to be over gunned, especially for a young hunter. Put more emphasis on good shooting than into the "cannon".
I do think a heavier bullet would be better if you were going to use it as a dedicated deer/antelope rifle though. From what I gather, using a bullet much over 60 grains, the twist rate becomes a factor.