I'm traveling from Las Vegas to the Lake George area of the Adirondacks in New York in mid-December, with my dog. I was thinking about driving through New Mexico and stopping in Memphis before heading North, since those are areas of the country I have not visited before. I'm guessing there is less chance of winter weather. However, since I'm not as familiar with those states, I was wondering what more experienced travelers thought.

What are your suggestions for routes?

Will I need snow tires?
My mechanic has not yet been able to find snow tires or all weather tires in our area for my Toyota Corolla.

Any other recommendations?
It's just me and my dog, so suggestions for individual travelers are appreciated. I'm planning to drive about 6 hours per day to make sure I stay well rested and alert.