I stop riding when there's ice on the road. Other than that, collecting and wearing military motorcycle riding attire keeps away winter's chill. The Sportsman's Guide has supplied military surplus items such as East German military motorcycle mittens, French military motorcycle overpants and matching storm duster (for use only on scooters).
A pair of handlebar covers similar to Hippo Hands is useful for Cold Weather Challenge rides < 20 degrees. One ride at -3 degrees caused the grease to solidify in my speedometer front wheel drive gear unit but MoS2 grease remains fluid at very cold temps. German motorcycle mittens have huge horse hide gauntlets that fit over the largest cuffs.
Air-cooled two-stroke engines seem to run well in the coldest conditions. Very lightweight mopeds with large wheels are recommended for winter rides because potholes can swallow a scooter wheel.