We wouldn’t repeat ‘it’s’ It’s snowy and cold. (Very natural, but the word ‘snowy’ isn’t a precise way to describe the current weather. You’d use it more for general climate) He winters in Florida because it’s snowy and cold in Quebec. Describing a current snowstorm, you could just say ‘There’s a snowstorm.’ (To most people, ‘snow’ implies ‘cold’. But those from a cold climate could have a lower threshold.)

It's freezing

You could say, "It's freezing." Or, "it's wintry."