Parowan Canyon and the traction law
Parowan Canyon is the part that deserves respect. Highway 143 climbs 3,946 ft in 15.7 miles from the valley, the steepest sustained two miles average close to ten percent, and UDOT classifies it as a Class II traction-law segment, a step above Highway 14. When UDOT activates the law there, four-wheel drive alone is not enough: a two-wheel-drive car needs tires with the three-peak mountain snowflake symbol, an all- or four-wheel-drive vehicle needs M+S tires on all four corners, and anything else needs chains. The statewide minimum tread is 2/32 inch; the 5/32 rule people quote belongs to the Cottonwood Canyons and does not apply here.
Highway 14 from Cedar City to Duck Creek, by contrast, is a Class I segment, where the law applies to vehicles over 12,000 pounds. Passenger cars are not legally required to carry chains there, which is a point our own winter driving page makes at length; we still recommend snow tires for the whole plateau from November to April.
UDOT plows Highway 143 during daylight hours, and the NPS puts it plainly: snow tires or chains are required on Highway 143 generally from November 30 to March 1. The live strip below carries UDOT’s surface condition and restriction for the “Parowan to Brian Head” segment when its feed is up, and the winter driving guide explains what the categories mean.