The Arkansas River Trail is great any time, but it’s a perfect solution for your winter riding needs. In Little Rock, it’s legal to ride at night, and a basic headlamp (along with a tail light for visibility) should provide enough extra light to travel safely along the wide, paved path. There’s a brief section that follows the River Road, but for the most part, the River Trail is only open to pedestrians and cyclists.
The Fast Girls Slow Guys cycling group uses this route for their Tuesday night winter hill climbs. To get to the start, take a left off the river route just past the skate park and head up the hill toward Fort Roots. The climb is just right for a set of low-light hill repeats. After all, a longer hill would mean more speed on the downhill: probably not necessary in the dark.