Snow tires on all four wheels keeps you from needing chains most of the time. When roads get bad enough to need chains on 4wd vehicles, most roads get closed.
If you are towing a trailer, you may be stopped by the Highway Patrol and forced to use chains even in moderate snow conditions with 4wd.
I don't like using chains, because they can beat up your wheel wells and require low speed operation, but I carry two sets for all four wheels when in the backcountry. Fall hunting can you stuck in places that are hard to get out of without chains.
You need to care if your tires are snow rated so the Highway Patrol will let you pass. The sidewall needs to mention snow, M&S, all season or some other buzzword to qualify.
