Lots of good advise.
I carry 2 sets of chains for the van. I've broken a set before towing, so now I like having a spare set. And if it turns to heavy freezing rain, like the Columbia River Gorge gets (inches of ice, always topped with a layer of rain water, with gusty winds) then chaining up the steers is the best way to maintain a reasonable speed.
I've found premium cables work best on the trailer. The trailer is pretty easy on them (3 seasons so far, and they look new still) but the nicest part is the tensioning ring-bungee means I don't have to stop to re-tighten them after install. They are also Super-z rated, meaning they only need 1/8" clearance at the sidewall, which is good because the trailer shocks are fairly tight to the tires.
Engine braking can help hold your speed, reducing the need for service brakes, but beware that can also exceed available grip, and cause a jackknife. It's very counter-intuitive to get out of that situation when it happens, because you have to give it a little throttle to get the slipping tires back up to road speed.
Also, I didn't see it mentioned yet, but traction is the worst near freezing! I'll take towing at 0-degrees any day vs 30 degrees! Once it drops below 20 chains are rarely even needed.
I leave my trailer brakes set as-is. Never had an issue there, but I do sometimes give it a little extra manual braking on steep downgrades.