This is a little bit tricky tho. You can make clothing look wet by adjusting the glossyness, making the clothing a little darker and maybe little bit see through depending on color.
But snow is a little bit more tricky. Since you need to adjust the clothing textures aswell. This mean you have to make a new texture with snow for each clothing piece you want to use.
It is possible but not without adjusting the clothing textures.
We do also have snow available on the VaM hub, but it doesn't stay on the character.