Thanks for the responses everybody. I don't believe I'll be needing to use the chains on any paved roads, these will simply be for muddy roads when hunting. The chains/cables will help the trailer to track behind me, rather than taking its own path to a possibly unfortunate end. In the past ten years, all of my experience with chains has been the big mud chains used on oilfield tractor-trailers. I've never had much experience with the light-duty stuff.
Looking at my trailer, I feel confident that I can get a set of chains or cables on there without any issues. I'll look at that website suggested by rotorhead and report back (good or bad) if we end up needing to use them. Hopefully I'll have nothing to report. I'll be hunting elk all next week south of Jackson, Wyoming with the TT, and the possibility of bad weather up in the high mountains during the month of October is fairly high. Fingers crossed for good roads.