Yes, 4wheel drive or not all vehicles must carry chains. R2 conditions two wheel drive cars must use chains and 4wd with m+s rated tires must carry them. R3 conditions even 4 wheel drive vehicles must use them. Weather conditions change rapidly up here and icey road conditions prevailent specially at night.
If you want to get stuck then I suggest to put the chains on doesn't matter you need them
No
Usually No, unless the snow is pretty bad
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