our serious Toyota 4x4 FJ Cruiser with the best traction tires (with studs) can handle most situations here in remote eastern oregon when used on plowed (but never salted and rarely sanded) paved mountain roads.
in deep snow-over-ice on unplowed roads, chains are necessary.
we've found that none of the fabric or cable style "chains" hold up for very long (read: short range emergencies only). we now only use all-steel chains (with cross links for ice gripping).
but this time of year when even the FJ can't make it to the house chained or not, we keep a fully chained-up old 4x4 pick up with high ground clearance at the ready. the chains on that one are extra-extra-heavy-duty modified semi-truck chains with swivel tighteners. only the pick-up has the fender room to handle such chains. these are the only chains that have held up to this sort of rough/hard use, climbing miles of our rocked-in mountain jeep-trail.
at present the snows are deep enough that we must leave the "road vehicles" at the bottom of the mountain and can only get in/out via the old pick-up. if snows get much deeper, we'll have to horseback or snowshoe the rest of the winter.
the joys of wilderness living!

taken a couple years ago of my gal saddling up to go to town when the chained-up pickup could no longer get through