hey mjr88 , I have been collecting .22s all my life and love shooting them. officially you should clean your guns every time you use them, all propellants are corrosive ad will eventually wear out your barrel. and as far as bore snakes go, as long as you pull from chamber to muzzle (that goes for cleaning with a rod also) then you will not harm your crown (just remember your crown has to be crisp for accuracy, and any contact with anything that rubs against that crown will deform it over time)
all that being said i do not thoroughly clean my .22s every time I shoot them, I use a bore snake