Some sort of limited slip will be mandatory, IMHO, on a 4x2 dually. Not enough ground pressure. Most of the weight on an empty pickup is on the front axle. I've used almost every type and each has it's plus and minus. I'm with Kettner with the Detroit Eaton True Trac. Torque biasing means the axle actually delivers traction to the wheel with the most traction, not the other way with an open diff. Since I only wanted it for snow, ice, and sand, I installed one each on the front axle of my Dodge and '99 Jeep not-so-grand Cherokee. They both work exceptionally well in snow, sand, mud and generally poor traction situations. Of course, they both have a rear L.S. also: the truck has a tried and true, Power Lok limited slip,(cone shaped wet clutches are under high preload so don't break away easily) and the '99 XJ has the factory track loc. (aka: trash-lock) They don't last more than 60K miles in normal use. You may think it's working, but it is slowly degrading.
Unfortunately, a 2WD dually is the worst of all platforms on ice and snow, especially with no weight in the bed. Very skinny actual snow tires with lots of siping will help some.
Because we never get our axles twisted up, like hard core jeep-types do, a full locker won't do you much good. This has been hashed over and over on this forum.