My $.02. I ahve no doubts that the 22 mag. can kill deer sized game. I read a very good book written about a plane crash survivor that made it out of far north western Canada in the dead of winter back in the 1950's ... he had a "survival" rifle in 22 LR., with which he dropped a mature cow moose. No body I know would based upon that incident of taking a moose out of necessity that the 22 LR is a moose cartridge !
Likewise, legal or not, the 22 Mag. in my opinion is not a "wise" choice for deer sized game. My personal minimal would be the almost forgotten 6 mm Rem. or the popular 243 Win.