I'd say you should be traveling early enough in the year that winter weather shouldn't be a big concern. That said, it's pointless to even try a guess at the conditions 3 months from now. You could hit snow, you could hit tornados, you could find perfect weather. Every single highway in the US is at risk of seeing severe weather on any given day.

The only thing we can say accurately is to look at the forecasts in the days before you leave and pick your route based on that information.