I haven't seen partridge do this, but I'm not surprised.
I have seen sharptails do this numerous times. Once there is snow cover they frequently have a dusk "last flight" where a loose flock will crash into the snow burying themselves for the night. The main theories are that this both insulates them from nighttime lows, and blocks scent release to predators with noses. I've also had sharptails flush midday from beneath a foot of undisturbed snow (it had snowed overnight) atop a wheat field, and upon investigation found actual lateral tunnels up to two feet long where undoubtedly the birds were feeding on waste grain entirely out-of-sight. A foot of snow still gets some light penetration, so the grouse were probably just finding the grain by sight after getting familiar with the field before snowfall.
