If you can get the latest information on when they open the road to the public from the department of highways, I found that to be the best time to go.
They have to wait for the 2 rivers to be free from ice so they can run the ferries safely. Leaving as soon as possible from the south,
usually end of may, or into june, is supposedly one of the driest times of the year, and although there's a healthy bunch of mosquitos and
horse/deer flies, it's not as bad as the hoards later on. When I went, the road beginning at the Klondike Inn was almost as good as a paved
highway, smooth and dry all the way to Inuvik. Unfortunately, a rain storm came through as I headed back down, which turned the first 150 miles
into slippery gumbo with patches of raw oil here and there. Be forewarned that there is only the "Eagle Plains" cafe/motel/bus stop about halfway,
and Fort Mckenzie 3/4's the way up, for facilities. Fort Mckenzie is not a tourist town, and is not very friendly to outsiders. It's a great experience,
and the scenery is nothing like you've seen before. You'll probably be all alone for most of the ride.