Cyclocross is a fall/winter sport, so they can absolutely do it with snow on the ground

Cyclocross National Championships here in Dane County, Wisconsin, in January.

In cyclocross, riders compete along a rugged course with obstacles that force frequent dismounts and require riders to carry their bikes while running up stairs and steep hills and jumping hurdles. The rider who completes the most laps in the time allowed wins.

Surely, you're at least tough enough to be a spectator:

“You can often see the majority of the course from one single spot, which is something we just don’t get in road racing or mountain biking,” Smith said. “It’s very welcoming and casual.”