Deep snow over 3" is tough, you need the fattest deepest lug tire you can get. Studs wont help for deep snow. You also need to run them at very low PSI.
I ride for fun in deep snow and use a 29 x 2.4 mountain king at 18/19 psi. I studded them myself because I do ride on frozen lakes and no body makes a big fat studded tire.