Altitude is not your friend in the winter months...one reason why I carry a road atlas when traveling. I've never used GPS.
Weather reports are critical to travel. That said:
I've spun the tires on my dually on the Interstate in AZ in April.
Been snowed in 2 1/2 days in WY in September, Interstate closed.

My advice here is to take a southern or lower-altitude route if at all possible.