Any winter cross country trips I would recommend I-40 over the bad weather more common on the I-80 Journey. If you watch the weather as you travel, you can head south on any of the following interstates that intersect I-40 if the forecast gets bad for the I-80 ride…and it often does. Use I-65 down to Nashville…then Paul’s comment on the Hays Smokehouse in Lexington TN is valuable. I don’t care for the I-55 run from Chicago to Memphis, but it is do-able, Then there’s the I-35 from Des Moines down to OK City. and finally I-25 from Cheyenne down to Albuquerque. Any of those roads can get you down to I-40 where the weather is quite a bit milder (usually) than it is on the northern route.
If it were my trip I would do I-55 from Chicago to St Louis and then I-44 down to I-40 in OK city…shortest distance and best compromise on weather potential! Lots of roadfood on both I-44 and I-40.