In our snowy travels here in North Idaho include pushing into unplowed but not gated public lands and campgrounds, 4wd gets us in, and chains occasionally go on to get us back out. Rarely do they go on on our way in. The are in effect a safety. We run a big truck camper, and dont do any aggressive trails, just push into areas that most avoid during the winter.
Chains are a game-changer though for any good 4wd. Doesn't really matter what tires you have, with chains a proper 4wd is a monster, be it snow or mud.