An empty DRW has LESS traction than an empty SRW. The reason? Roughly the same amount of weight over the rear tires, only twice as many tires.
A DRW loaded to capacity will have MORE traction than an SRW loaded to capacity. The reason? Twice as much weight over twice as many tires.
2WD will get "stuck on wet grass" when you run smooth road tires, don't have a locking differential, and/or have an heavy left foot. More often than not, people create their own problems by romping on the accelerator in sketchy traction situations. I can break a 4x4 loose on wet grass. All I have to do is slam it in gear and stomp on the gas, and I'll be as stuck as any 2WD that does the same thing.
If you're going to be where the traction is sketchy, run traction tires. Don't expect to be able to move in slick conditions without the weight of the trailer over the rear wheels. Make sure you've got a locking differential. For those rare times when you do get truly stuck, have a good tow strap behind the seat.