Snow, in and of itself, doesn't really change anything with regards to the sleep system.

10*F is 10*F with or without snow on the ground.

You do need a tarp for the snow but I am assmuing you have one already.

You do need to keep the snow out of your boots [gaiters or high boots].

You do want to wipe snow off of your body/clothes/gear fairly frequently since it will melt due to your body heat.

Love hiking with a gentle snow fall. Magical.

High 20s low 30s with wet, slushy, snow and icy condtions are tough. I usually stay home or just dayhike if those conditions are expected.