I would say chains will help a lot. When I lived in Laramie WY for a year I got to play in a lot of dry snow. I could go through it just fine as long as the snow was under my front bumper, with dry light snow axle drag does not slow you down much unlike mud or heavy wet snow will.
Always bring someone with you with another rig! I always bring a sleeping bag and some food just in case, and of coarse very warm clothes.
Chains will help even in deep snow although they are a major pain in the butt. You might carry a pair and never use them in an off road situation. I've ran in 4-5 feet of dry powder with good tires.and airing down to 5lbs -+. The more horizontal the lugs/crossbars the better they work in deep snow. The problem with that type of tire is that it isn't very good on icy/snowy maintained roads.
I am no expert, but here is a picture of my mine and my friend Kevin's TJs sitting on about 5 feet of snow. Both are on 12.50 tires with about 8# of air.
This was late snow though and not dry powder. We did much better in this type of snow by not using a lot of power and trying not to break through the crust. Slow was the way to go. I suspect that deep powder can be much different though.
Later in the day, we pull off to air up. We were about 1/4 mile from the plowed road. I was stuck twice in that 1/4 mile and had to have tug. Low tire pressure is very important.
"At what point, then, is the approach of danger to be expected? I answer, if it ever reach us it must spring up amongst us. It cannot come from abroad. If destruction be our lot, we must ourselves be its author and finisher."