UV protection simply means the lens blocks UV rays.
Polarization is glare blocking. I won't buy unpolarized sunglasses. However, for goggles, the only time I prefer polarized lenses is on bright days with good snow conditions. In flat light, they tend to wash out the terrain and in poor snow conditions, you can't spot icy patches because the glare that gives them away is blocked.
"People say that marijuana smoking is going to get in the way of my career. I say to them that on the contrary, my fighting career is getting in the way of my marijuana smoking." -Nick Diaz