If you are claiming the Jeep would be able to pull it out, that tractor will do it without breaking a sweat; unless you are talking a lawn mower/play tractor... Also not sure the truck you have, but if it a newer open diff with traction control, it will likely be better than your Jeep per being heavier and being able to grab for traction. It won't matter if you can lock all up on the jeep if it can't grab.
Anyway, you don't get much snow there, right? If you have very little, it still gets cold enough to keep that ground hard, so you could go even earlier in the season, or wait and get lucky for a spring cold front that will afford the same thing.
You can also let some air out of the TT tires as to provide better flotation than dragging a garden rake through the mud. As others have said plywood, or 2x6's are a good backup plan, but if it is so mucky that tractor can't get it, then you are risking damaging the suspension on that trailer per your attempt. In that regard, you should know if you can pull it out just by your drive in to retrieve it.
