WA 20 usually closes around Thanksgiving (depending on snow fall) and US 2 is open year-round but sometimes has temporary closures do to snow removal or avalanche control. These usually only last a few hours but can last a day or two.
Both of these routes are gorgeous. We make the tirp over US2 many times every year.
I can't choose just one! Pick the one that takes you the route that sounds best and you'll be fine. US2 is shorter but WA20 is more scenic.
If you go WA20, you have to stop in Winthrop for icecream!
