Like for kayaking and snorkeling, winter surfing requires the right gear - namely, a wetsuit or drysuit. Surfer Michelle Sommers, who surfs all winter even when the temperature drops, recommends wearing gloves, boots and a hood. The best part is that in some spots, the winter months bring better swells than in the summer. So not only will you not have to share the water with a crowd, you'll be getting the best surfing of the year.
As with parkour, snow and ice can make BMX riding harder and easier at the same time. Pedaling through deep powder isn't going to happen, but if you've got a mind to, with a little work you can build your own jump, complete with a cushy landing zone.
For those really serious about riding in the snow, there's always the Ski Bike, with short skis in the place of the wheels. They're available for sale, but why not build your own, with directions from Instructables?