Rural King sells their brand of UTV winches that are pretty well priced. 3500# is around $169 and 5500# is around $199.
I am considering buying one to rig up to the front or back of my GC2400.... Looks like the GC2400 is around 1400# dry weight. I have a fairly steep hill that can get slick. I would like to have the winch to help get the tractor up it, if needed.
IF I'm understanding your question, You are just needing a bit of help getting up a slick hill, not trying to pull yourself out of a situation where you are deeply mired in mud. If that's the case, you might want to consider a decent set of chains, rather than a winch. There are some good threads here on TBN comparing the pros and cons of different chain styles that may be of interest.
4-link V-bar/studded ladder style chains gut me up my icy driveway in the winter.
Pros: Relatively inexpensive, easy to mount, provide good forward traction
Cons: (1) the ride was a little rough (but bearable) on asphalt or hard ground when moving at higher speeds (I have filled rear tires. Ride would probably be better with just air in the tires, but I needed the extra weight for traction.) Lateral traction was not so good, so operation on side hills or on very uneven terrain in my woods was a problems. The "grip...slip...grip...slip" tendency of a four-link ladder style chain can damage pavement, especially for studded/v-bar chains. Going to a 2-link ladder style would improve this significantly, and would improve traction in general over the 4-link style.
DuoGrip chains: I got some studded DuoGrip chains to address the problem of poor lateral traction when working in the woods. The ladder style just was not cutting it. Pros: Forward traction was as good as the ladder style. Lateral traction was much improved. Worked well in the woods on sidehills and uneven terrain. Cons: they had a really rough ride when operating on hard surfaces. If I was going much faster than walking speed, it felt as tough I was going to shake myself and the tractor to death. I'm not sure if they make these in a size to fit your tire.
"Euro style" chains: Since I needed to drive my tractor sometimes several miles over pavement or hard-packed dirt roads and wanted to be able to travel at faster than walking speed. Pros: smooth ride, excellent traction both forward and lateral. I have not had trouble with the studs damaging paved areas - probably because the tration is good enough and continuous, so you don't spin tires easily. Cons: expensive, may not be available in a size to fit your tires?
Another style to consider (which i have not tried myself) would be two link ladder-tyle chains made with square chain. The square provides more "bite" than the traditional round (non-studded) chain, but is far less likely to damage pavement. THese are made in a size to fir your rear tires.