For the decorations, use white for one color, for snow of course, and pair it with another color you would like to use as well. Since you are emphasizing the winter time frame, if you go with a 1st Birthday theme, you may want to keep it on the generic side.
Hang snowflakes from your ceiling at different lengths.
Decorate the party walls with big snow people that you cut out from large cardboard and other wintry items, i.e. mittens, hats, scarves, etc.
Cover your furniture with white sheets
Place Styrofoam packing peanuts around the party room for the snow
Create the look of a frozen lake by placing clear plastic bags on the floor.
Place a sign stating, Danger: Thin Ice!
Hang twinkly lights all over the party room.
Make snowmen out of balloons; taping three different sizes of balloons together and decorating their faces with markers.