Wobbly Steering Wheel

Please help! My 2005 Honda Civic just made it through a blizzard (outside the whole time). This morning I started driving it, and whenever I got above 45 mph the steering wheel started vibrating / whobbling very badly. My car seat was also vibrating. I poured hot water over the rims when I got home and that did not seem to help. Should I take it to a car wash? Is my car safe to drive? Thanks!!

Parking indoors in a heated garage overnight beats a car wash. Chances are there is a build up affecting wheel balance.