The turn off to Cedar Breaks is the high point on 14, with the park itself being a bit higher. Further north on US143 you can turn off onto a gravel road to the top of Brian Head, one of the highest spots in Utah that you can drive to. Beyond that the highway passes the Brian Head ski resort.
So the ski resort and the park are best sources of information on snow conditions in this area. The road through the park is not plowed in winter, but 14 itself is plowed, as is 143 to the ski resort.
20 is the easier way across this range. But if you are comfortable with mountain driving, you'll handle 14 just fine. And if you want to seek the Breaks, then 14 or 143 are your only options.