Is there a snow god?Depends on your belief.
In Nordic mythology we have Ull and Skadi who are strong in the winter.
Ull is an Aesir. He is a hunter and is known for his skiing.
Skadi is a Jotun. She is married to Ægir of the Vanir. Skadi is known for her love and prowess for the winter time and the snow covered mountains.
The act of making it snow is sometimes connected to the Jotun King Snjo.
I think the Same and Finish religion also have som gods that like snow.
And the Inuit beliefs probably have many too.
Now it's Russian parallel to Santa, but the origin is Frost - the lord of all things cold, the ruler of snow storms.