I have both 3500 DRW and SRW. I live in Idaho about 90 miles from Yellowstone to give you a geographical context to my experience. I have traveled many miles in the snow with DRW including working on the top of the Big Sky ski resort during the Winter. I would have to chain up to get heavy equipment to the top of the hill. I chained the back outside tires and fronts. I have always run an aggressive tire on the these trucks (Cooper SST, Kelly TSR and Kelly MSR). If you chain up they are not bad pushing deep snow but not as good as SRW. When the DRW really sucks is when the roads are rutted and iced over, they throw you around as the duals try to find a home in the ruts. The SRW 3500s clearly are superior in the Winter but DRW is workable just not as pleasant. Loaded they are better in the Winter than when they are unloaded.
During the Summer off road with a DRW my issue is the fenders suffer from brush scrapes that SRW are not exposed to. The other issue is the DRW beds are made of composite plastic that when cold are brittle. They shatter when hit. I prefer the SRW for most everything. The DRW's are great for going down the road at max GVW and outside of that I don't find them that agreeable. If you "need" the weight carrying capacity, than go DRW. If you are considering going to DRW for added capacity but it is really not necessary I would go SRW. The new trucks are rock solid in SRW. The tires are better, the suspensions are better than they were 10 years ago.