The bulk of your trip will be beyond the I-81 corridor. Early to mid-October is usually a glorious time in the western states. Though snow is not unheard of, October is not one of the snowier months here in the west. I was in southern Colorado and northern Arizona (north of I-40) in early October and the weather was incredible. Nice days, crisp but not overly cold nights. Further south was even better, from what I was seeing from the forecasts. I think your timing will be a factor, if you're leaving the eastern seaboard and are heading west on any of the routes mentioned by mid-October, you should have a wonderful trip. Mother Nature can be fickle at times, so keeping an eye and ear to weather forecasts would always be advisable.