Replace the front fork, move the pivot point down as close to the ski as possable, and incorperate a spring that lifts the front of the ski if it becomes airborn.
Front Ski should have a surface like a cross country ski, to resist sliding backwards.
the rear should be wide, around 6 inches. the back wheel should be plastic with blastic mags instead of spokes. the mags should be as wide as the wheel, but curved and thin so they alow the wheel to deform easy. when sitting on the bike on hard ground, the back wheel should be flattened for about 1 foot of it's leingth. The tread would be similar to automotive snow tread, but with smaller blocks and shallower voids.
chains can ice up or get clogged with snow, so it should be shaft drive
Brakes would be a rear drum brake to avoid snow buildup.
Over sized hand grips for use with snow gloves.
A half fearing fender in the front of the rear wheel to keep it from throwing snow against your calves and down the top of your boots all day.