Is this a bad time?

Keep your fuel topped off, don't let it drop too low. I have been stuck in road shutdowns during the winter on I-40 in AZ, NM, and TX. It's no fun sitting in a cold car for 8 to 12 hours. Some warm weather gear doesn't hurt, either, or at least a few blankets.
I've also been in HEAVY snow east of El Paso on I-10, but don't remember it sticking on the road, just screwing up visibility.

 

Just like you will in a big rig, do a thorough Pre-Trip Inspection. Fluids topped off, any questionable belts or hoses replaced, tires/brakes inspected, tires fully inflated, all lights working, etc.

Then make sure the emergency supplies are there: jack, lug wrench, & (inflated) spare tire, first aid kit, flares or triangles, fresh water, emergency rations, blankets, tire chains if the route could possibly call for it, map/atlas, cell phone, basic tools, tape, etc.

As far as i40, I wouldn't have a problem running it. You may encounter snow if a storm has passed through, but if you're ok waiting 6-48 hours you can just get a room and let it pass.

 

I thought this was a big rig forum.

 

If you have to ask this, park it before you cause the next 190 vehicle pile-up.

 

Don't wait for the roads to close. If you feel its unsafe for you pull over, take a break, get a room. Taking frequent breaks allows you to unwind. Its going to be stressful for you. You may not know how tense you are. Tenseness leads to over reacting to a situation. Keep all your windows clear. Don't pile up the car where you can only see out the windshield. Another thing no one has mentioned yet. Keep your cell phone charged. Not full proof cause you can still be in a no service area. But a dead phone will never do you good.
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If you go I-10 to I-20 all you got to remember for directions is follow all the signs that say I-10 E. Thats it. YOU still need to look at a map to know what big town is next in case you are confused by the I-10 east signs. If you know your supposed to be in El Peso next it cuts down on being unsure.

 

I live in Orange County, CA and have driven to Arkansas many times during the winter and in a variety of weather and road conditions. You will be okay and enjoy your trip if you use common sense. Pay attention to the weather forecasts during your trip and act accordingly.

Not sure if someone already mentioned:
-Make sure your tires are in good condition
-Make sure your windshield wipers are in good condition
-Make sure your wiper fluid (and all fluids) are topped off
-Bring jumper cables
-Bring an ice scraper and snow brush
-Flashlight

Have a great trip and honk when you pass Quartzsite, AZ - - - I am camped just east of the Love's truck stop.