Percentage wise the added payload of a 2WD can be quite a bit. In my 2004 Duramax 2WD I think it is 370 lbs.
When we were towing a fiver, I did have issues more than once on wet grass. I always got out, but it's a bad feeling when it starts slipping instead of going. If we were to get another fiver, I would not hesitate to use the 2WD truck. But if I was buying from scratch for the purpose, I'd buy 4WD, no doubt. If I needed more payload because of the 4WD weight penalty, I'd buy more truck.
Finally, winter was a problem until I bought dedicated snow tires. Or carry 300 lbs or so behind the fenderwells. That worked well too and had no effect on handling.