There's no way to pre-play the particle effects, so Sushin is right - you'll have to find a workaround.
Is it always snowing in your game? Would you say that it's snow-themed? If so, I'd suggest that you make your snow particle system global (i.e.: it's not destroyed between layouts) and place it in your initial title screen (just mock one up for the sake of testing if you don't already have).
Actually, thinking about it now I'd say you could even generate the particle system while the game is loading. If you'd rather not have it look like it's there, then just set it to invisible. Read about custom loading screens here.