Yes, if enough snow builds up it can keep wheel from turning.
If you are lucky tie rod (inner or outer) has to be replaced. If you are not lucky you will have to replace all steering mechanism (steering rack).
Steering fluid leak.
the most likely cause of that would be the power steering pump failing.
No it would not cause the pump not to work, check the fluid level, if low fill it to full mark and test steering,if it still doesn't work the system may need to be bled to rid it of air built up from steering the car without the pump running.see a mechanic.
Power steering belt slipping?
* No power steering fluid in reservoir * The power steering pump is not operating
A front suspension system has excessive steering effort and rapid steering wheel return. The most likely cause of this problem is
Check out the bearings in the steering column and the knuckles in the steering shaft
ummm power steering
No power steering fluid, broken pump, or broken lines.
Bad coupling from the steering wheel to the rack & pinion or steering gear. Faulty steering gear
no