Get rerouted. See if they can get you out via SLC or even LAX on DL/KL or AF metal. Avoid SFO as they too are expecting winter weather (in the form of rain, not snow, but could still yield delays).

As of right now, loads on BZN-SLC tomorrow look decent for all flights (at least Y2). Try BZN-SLC-CDG-ZRH with DL metal up to CDG and AF from there. SLC-CDG segment looks good too. J and Y on that flight are wide open!

Edited to add: while there is not a current weather advisory, I've had good luck as a PM calling up and explaining the situation. As long as there are reasonable alternatives I've usually found agents eager to be proactive. If you don't get the answer you seek, be polite and then call back.

Alaska currently DOES have a travel advisory for SEA so if any of your flights are on AS, you may qualify for the reroute.