Craig,
1. Hot Sox don’t provide enough of a “shell” to resist compression by the snowshoe binding. You’ll have to really crank the binding down (to keep the foot stable, see #2 below), right to the surface of your foot. Result: cold feet and poor circulation.
2. Hot Sox don’t provide enough of a stability platform for climbing and traversing. As such, your foot will slide around relative to the binding sole. Result: extreme fatigue. This can be a problem even with soft footwear like trail runners and mukluks, it would be a nightmare with Hot Sox.
I haven’t personally tried this.
I have used NL’s with trail shoes (variety) and mukluks (Steger Arctics) and have made these observations with both, with trail shoes getting the nod as more appropriate than mukluks for steeper terrain.