They keep that road maintained pretty well, you should be fine. While I have personally never chained up a trailer before, I have seen it done a few times in the past-but on tandems with brakes. I did watch some idiot last winter towing a huge boat across Stevens pass stop in the middle of the highway to chain up in a near blizzard. I couldn't tell if he chained the truck or not, but he was putting chains on the boat trailer. This was a 3 axle unit that I'd been following for a long while. Gusty winds, driving snow and overall really bad conditions. I was actually thankful I was in the Subaru and not the Jeep during that storm, with my wife and baby. I saw no issue with his truck or trailer, no signs of any particular driving hazards or safety risks for him or the trailer-at least that I could see while following him. I THINK he was just being cautious as to what was ahead. Don't know, didn't stop to ask. We made it around him in the deep lane, then continued on without issue of any kind.
I have heard old guys back in my rodeo days who chained up stock trailers, and my cousin did occassionally at the ranch moving animals in the winter. Of course, these are large stock trailers loaded, and with brakes on all axles. I never did see any issue or need to chain up, but he did for some reason.
For what you're doing-I wouldn't worry about it. I've towed many trailers of all makes and models with all kinds of tow rigs over the years and I personally have never chained up-on the trailer. With no brakes on the trailer, I don't see what good it would do anyway. Where you're going and the roads you'll be on, there's no "off-camber" to worry about and the states do a pretty fair job of keeping those highways clean. I wouldn't hesitate in the least to tow and not worry about chaining up. I think semi-trucks were mentioned earlier-our semi's at work have locking diff's and when the snow is bad here, they chain EVERYTHING up-all wheels on truck AND trailer. We do get a lot of ice here though and freezing rain, freezing fog and all kinds of other nasty wintery stuff that's no fun to deal with.
All that said, you have a very nice looking setup there! Love the color match Jeep/trailer setup, it looks great! I'd love a trailer like that painted to match my Jeep, just can't afford one right now.
Be careful towing through the winter-you obviously can't go as fast as a nice summer day and I tend to be much more alert when towing in winter months-mostly always watching out for the "other" guys and keeping my distance accordingly as deteremined by road conditions and weather. Be smart and you shouldn't have any trouble at all.
Best of Luck,
Mike
