Oh no, you've awoken the sleeping weather nerd inside of me, so buckle in!
So NEXRAD does show snow/winter precip. I think the question you're trying to ask is "why is it not classified as pink, purple, and blue on my on board radar?"
There's a few things we should go over
First, you're looking at overall return vs hydrometeor classification, a fancy way of saying "is the radar beam hitting rain, snow, sleet, hail, debris from a tornado, or dust?"
Without getting into the admittedly complicated science of dual polarization radar, it comes down to having that automated for us in two layers. The normal reflectivity mode which we all know and love: green, yellow, red, purple, pink, and white for intensity of precipitation. That goes with the assumption that you're above freezing. Notice I said purple, pink, and white - those are classifications for particularly intense precip within very strong storms, aka hail. But a normal radar can't see hail and immediately recognize what it is, it only sees whatever is in the storm. Hence the "debris ball" of particiularly strong tornadoes, like the May 20 Moore OK EF-5.
