You realize, of course, that spinning your wheels will not get you unstuck . . . However, it could snap an axle if the tire suddenly finds traction.
And yes, after getting into deep snow and then moving up to highway speeds it is not unusual for the wheels to have clumps of snow that will make a vehicle feel like the wheels are out of balance. I've had it so bad I thought something was wrong with the vehicle, like a loose wheel, but no, just snow in places it doesn't normally get to. Find a warm place to park where it will melt, or get under there and clean it all out.