What is that - two days through B.C. plus two days through Yukon and Alaska... each way, allowing for an enjoyable pace? Sounds like a spectacular trip, but it would be good to have a substantial allowance for weather-related travel delays. The term "quick visit" doesn't jump to mind.
My concern if caught in an early snowstorm would not be just tow vehicle traction, but trailer tire traction. It doesn't matter that the tug can pull and turn if the trailer is swinging around like a pendulum. I think if the road condition is such that chains have to go on the tug, the trailer doesn't belong on the road with typical trailer tires (which are summer tires, not even all-season).