I 40 From West coast to East coast in Oct?

I-40 stays open year-round from California to Wilmington. Any part of it can be snowed upon, but this is not likely in October, not even across the higher altitude sections in Arizona and New Mexico. October is way too early for snow at I-40 latitudes across the Great Plains and the Mid-South and into the Appalachians.

More into winter, it can snow, and they clear it. If there are closures, they are short, and usually because of blizzard conditions on high plains making safe movement almost impossible. But this is more likely December-February, not October. Across the mid-South, freezing rain making for icy roads is actually the more typical winter weather along I-40, but again, not in October. Storm systems moving through at that time of year are more often heavy rains and high winds, occasional swarms of tornadoes, a repeat of spring weather patterns.

You can get high winds at any time in eastern New Mexico, Texas Panhandle, western Oklahoma. Prevailing wind direction is west to east, but changing weather conditions bring north or south winds, and these will be cross winds. Rarely is traffic stopped for crosswind conditions, but highway departments will publish warnings.

Temperatures are what they are. Flagstaff can drop below freezing or be up in the 60s. Amarillo to Oklahoma City might be as low as the 40s, highs up to 70s. On east to Nashville, lows in the low 50s, highs to mid 70s. Slightly cooler crossing the Appalachians, then slightly warmer as you come down off the Piedmont onto the Atlantic Coastal Plain, where October can be either comfortably cool or warm and muggy.

Your riskier weather for driving will be getting from the PNW to where you choose to connect to I-40, getting across the coastal ranges and high Sierra (unless you follow the coast all the way down to Southern California).

I wouldn't hesitate to make that trip in October. I can't think of any issues at all in October.