When you think about it, there's not going to be all that much chafing of a winch line, other than at the fairlead where it enters the winch. Everywhere else, it's a fixed line, not a running line. Fixed lines don't chafe much, and it would probably even be fine wrapped around a tree. If you want to be super-careful, I guess you could use a nylon strap around a tree, then fix to that, which is probably a heck of a lot less point load on the tree bark, too.
I would be sure the fairlead you're using in front of the winch is the best type for a Dyneema line, which might be different than the types used for steel cable. In fact, the soft line fairleads might just be an aluminum ring with a slot, and stainless steel rub points around the slot. That's the primary chafe point, in this application.
One excellent property of single braid Dyneema (eg. Amsteel Blue) is that it's super easy to splice the stuff. A child could do it, with pretty minimal training, and the splices are super strong... stronger than the original line, if done right.
