The Prius got a similar ground clearance (5.7'') than many other cars, almost the same as my neighbour BMW 328i (5.5'') and the exact same for Subaru Impreza (5.7''). Yes it's still low, but that's probably fine 99.5% of the time, and I am glad 99.5% of the time that I got rid of my SUV! The center of mass being lower, it drives better in slippery snowy icy conditions.. In the end, what's make the difference is the winter tires. I am not afraid to take my Blizzard Pearl in a snow storm!
I nearly got stuck Wednesday (3rd gen): plowed my way into a parking spot where the snow was a bit more than 8", and crusty. With a bit of back-and-forth, trying different directions of the front wheels also, I finally was able to extricate myself. It doesn't take a lot of depth, especially if it's getting packed. This was with 15" X-Ice tires too.
Does any snow get trapped in the front fascia? Or plowed by the grill? Seems like packed snow would damage the front end.
I would be very careful driving around pack snow. Perhaps it is less of an issue when you back the car as the rear end looks slightly higher.
Looks like you can still put foam pipe insulation in the front grill, two 1.5" OD tubes by the looks of it. That'll help some with snow I think, fill the voids, make the front more uniform. I've only got one tube so far on ours (3rd gen) this year (similarly, on lower grill), and considering temps are dropping to -8C overnight, daytime highs still below freezing, I should probably put in the second one. Temps are supposed to moderate though, so maybe I'll do nothing.