Not at all, polarizers don't help with flares and in fact, might make it worse. Flares depend on the quality of your lens. Primes tend to do better as the light coming through has less chance to bounce around in your lens. Manufacturers coat the lens glass with special coating to control flare and these typically make those lenses more expensive. Smaller aperture helps with edges - it works like your eyes. Keep them wide open and you see more of the edges. Squint and you see less.

This shot below was taken with a Wide Angle zoom lens (no polarizer) which is rated to have good flare chracteristics. There's still some flare but there are techniques to get rid of flare directly which I will do a write up and tutorial later when i have the time. Also, this is at f/22 (very small aperture) to create that massive Sun Burst which is caused by the diaphram of the lens.

Your snow shots are probably washed out because it fooled your light meter. Take your meter's reading then add 2 stops )) and yes polarizers help with snow scenes too )