So, you're walking in the snow and you slipped and fell. It's just a short fall, but why does it hurt so bad. You should be fine... right?
When you fall straight onto your bottom it is actually, roughly, equivalent to being in a 10-15 mph car accident, sometimes more depending on how you fall. Either way, that's a lot of stress going into your body. Once you contact the ground it is about 4 times the normal force going into your body.
That's plenty enough force to break a bone, bruise or tear muscles and ligaments, or put your body out of it's optimal alignment. The alignment is what makes you feel like your walking funny or standing funny.
To correct these types of issues takes time and effort. If untreated you can lose range of motion in joints, have long term biomechanical difficulty, and many other problems.
So, just because it's a small fall doesn't mean there can't be big problems. It is important to be evaluated by your doctor.