Starting from Cedar, take Highway 130 north toward Minersville. Go as far as you like. The first 20 miles or so are nearly flat, then you start a long gradual climb. You could turn off and go look at the petroglyphs at the Parowan Gap, maybe ride into Parowan and take old Highway 91 back to Cedar. If you like climbing, and don't mind the cold, ride Highway 14 up the Cedar canyon to where it's closed by a landslide. Maybe take the Coal Creek trail as far up the canyon as it goes, then hit the highway. Old 91 to Kanarraville or New Harmony is a nice flat few miles. Highway 56 west will take you into Nevada if you go far enough.
If you start at St. George, ride the Virgin River trail from one end to the other, about 18 miles one way. Snow Canyon is a nice ride, quite steep near the top, take the trail paralleling Highway 18 coming back down. You can always ride to, or near, Zion National Park. It will be more pleasant weather in St. George than Cedar this time of year.