It somewhat depends on what the "smaller" road really is.

During 14 years of commuting 100 mi/day in Colorado and listening to the police scanner for situational awareness I learned that the interstate gets first treatment for snowplows however it's also where bad drivers and semis go to crash in large numbers.

A secondary highway (US designation) may get nearly as good plowing from the county and far less pressure from crash dummies.

Anything less than a US-type highway would be a bad bet and the more remote from towns where the snowplows originate from the worse.

In my Jeep I often made it 50 miles thru blizzards and floods to be at the office when people who lived 3 miles away couldn't make it. (I treated it as a challenge while they likely saw an opportunity.....)