I have a 99 dodge 2500 diesel 2WD. It will get stuck on wet grass very easily, it's just a fact of life with the heavy engine up front and 2WD. I do have a limited slip differential.
I put all terrain tires, yokohama geolander ats, on the rear and it does help a good bit. It is not a cure all however, it'll still get stuck just not as quickly as before. Put some decent all terrain tires on the back, be diligent in assessing the conditions and you should be fine. You'll not be doing any serious off roading but you can go most places you have any business hauling a fifth wheel trailer. The key is to know you limits and not push them. You have to think ahead, can I move the truck from where it's parked now if it rains tonight? Etc.
I still have my old '99 dodge and it's got 384,000 miles on it now. It still pulls like a freight train and puts a smile on my face when I drive it. That being said, the Toyota Tundra I bought two weeks ago is a 4x4, that old dodge cured me of ever buying a 2wd pickup again.