Which route would you take.... Winter CA->TN

Planning a moving trip to Tennessee from CA.
Truck: 2005 4x4 sr5 new toyo AT2 tires, going to haul a small trailer.
I was thinking taking 80 through reno till colorado and getting on the 70 after visiting a friend, but my aunt suggested going further south to avoid potential bad weather.
What route would you take?

Any advice on tools to bring?
Do I need a hijack, air compressor, warm socks? any ideas appreciated.

 

When are you planning on taking the trip?

 

January

 

I live in Reno. Usually the roads are fine over the hill but sometimes they're not. I've never had a problem when it's snowy I just use 4x4