[Next-day edit to correct how I used my penalties, and to use hvb's rack penalty from the next couple of posts]
My numbers are from
THIS thread.
From Burlington to Mt Baker in winter, you're probably not going to average over 60mph, so we don't need to account for a speed hit to your range. In fact you may be a little under, but to be conservative we will ignore that.
Temperature will cut you down. Let's say average temp for the trip is 29 degrees. That will take about 15% off your range.
3500' of elevation gain will cost you at most 35 miles on the way up. Then you'll gain at least 14 miles on the way back down. (Conservative guesses again).
Roof rack is the big question. I've seen a 15% penalty for a bike on back of a Roadster. [According to hvb below, the penalty for rack + heavy rain at 70+ was 47.5%. Wow, that's a lot. He will go slower, and let's temporarily assume no rain, so let's use 35% for the rack]
If you charge an 85kWh car to full in Burlington, you should start with at least 250 miles. It's a 120-mile trip, with 15 + 35% penalties which makes it effectively 180 miles. Add 20 miles for net elevation, and you will expect to use 200 rated miles of range for the trip. My numbers are kind of conservative so that should work...however, I didn't account for unexpected headwinds or precipitation, both of which can be big hits. If you get those, you will want to slow down. (Not below 45mph though, unless you also turn off the cabin heat).
It's still a good idea to have a backup plan, at least the first time you try it. Is there somewhere halfway back you can stop to get a boost if it looks like you are cutting it too close? Plugshare shows 120V outlets at Chair 9 Pizza and Bar (though if it's really cold, that may not be enough to gain range!), a couple of private homes a little off the main highway, and you can always head back to Bellingham before Burlington.