On what I can remember from my reading, the German initial spearhead into St Vith was on December 17, 1944. The weather conditions were bad, overcast; penetratingly cold; snow flurries mixed with rain; poor visibility with roads both muddy when it rained and slick when it froze. The terrain between the Schnee Eifel and St. Vith was rugged, forested, and rock strewn.
In your creation, you could go with either overcast or rain and mud or light snow. If I were doing this battle, I would use rain and mud. From what I have read and photos I have seen of this, the ground was muddy with a very light covering of snow. The mud was more a problem than the snow. Depending on how much or how little visibility and "fog of war" you want, choosing either overcast or rain can you give one or the other (how much or how little).
I hope this helps.
Bocko