How about enabling fog and using 2 different particle systems (or more). The first one should have big particles with a gray bitmap and an alpha value of 0.5 or less that simulates the foggy effect. The second particle system should have small particles (10%-5% of the size of the big particles) and a nearly opaque white bitmap, this would be the snow. Then adjust some values like speed, direction, amount of particles and alpha. I guess an aditional blur effect would make it look more realistic.
besides that, you can even enable fog effect on your map too. if you want more, you can even add motion blur effect so that when the snows fall it will look more realistic.
1) should the billboard follow the character? (set to children and parent)
2) At the start of the game, the particle emitter will move the billboards slowly to the scene. Is there any way to set the particle effect to move to the scene first?