I would suggest you start checking the extended 5 and 10 day forecasts on the Weather Channel before your departure and see what you might be facing in the way of weather and choose a route accordingly.

While it is true you could encounter bad winter weather on either the I-80 route or the "Route 66" route the chances of extremely cold weather would be greater going across Iowa and Nebraska than going across Missouri and Oklahoma. The southern route while roughly 150 miles further would give you the opportunity to visit Hoover Dam if you never have and see the magnificient new US 93 bridge over the Colorado River gorge.