I can only echo the good advice given so far.
As Thom said, timing is the critical element. Watch the storm forecasts and look for a window of opportunity where you can scoot through those problematic areas between storms.
Traveling between Texas and North Dakota over Christmas few years back I did just that, staying in Texas a few extra days to allow a storm system to pass through the Great Plains before I headed north. And I had no problems getting back to North Dakota. But I could surely see the evidence of the previous storm piled all along the roads on the way home.