As a former Kingman, AZ Resident and traveling that path hundreds of times, I'd say you
may or may not be able to make it all the way without some extra stops. As said already, WATCH your weather. Plan for extra time. Stop in Kingman and spend a day to let things blow over if you need to. Just east of Kingman at Seligman is where I-40 usually gets closed. But don't wait for the closure if you're pulling the trailer. If the truckers get off...I get off. The road closure is always a last resort and may be too late for you. Seligman has very little to offer in the way of accommodations - especially if everyone on the road is pulling off there....hence the reason I say spend an extra day in Kingman if you need to.
There are actually three (3) rims to the Grand Canyon. The North Rim is no where near I-40 so it's not really an option...even if it were open. The South Rim is the most popular and it could be ify at that time. On the other hand it could be gorgeous weather too. The 3rd option is the WEST Rim on the Hualapi (Pronounced: Wall-A-Pie) Tribal reservation. It is only about 2 hours from Kingman. The weather is almost always great that time of the year, as it is lower in elevation....about 4500 feet at the top. It is the home of the
SKYWALK. Although it is quite different from the South or North Rim, it is still a site to see. Ask at the Kingman Tourism Center for directions if you want to visit. Do not rely upon your GPS...it will take you 5 hours out of the way because it takes you to the tribal headquarters which is no where near the West Rim.
If you'd rather wait to see the South Rim, it is about an hour north of I-40 from Williams. You can dry camp in the parking lot over night or there are some RV parks just outside of the National Park. For a different sort of trip, get an RV Park in Williams and
RIDE THE GRAND CANYON RAILWAY up to the Canyon
From the South Rim, there is a short-cut turn off to get back to I-40 at Flagstaff.
One of the worst storms I've ever been in was in Flagstaff at that time of the year. but that was only once in 40 years. Sometimes it is just cold with left over snow on the side of the road and in the parking lots that hasn't melted yet. It can be very difficult to navigate a truck and trailer in some of those places and find a place to park if you should want to stop and eat or shop or something like that because of the amount of snow piled up from the snow plows. Flagstaff is a college town with a lot of traffic and very narrow streets. If it was me, needing to stop there with an Airstream, I'd stop right at Little America Resort on I-40. Full Truck Stop, Convenience Store, Motel, Restaurant, Bar and I don't think you can get much better.
East of Flagstaff to Holbrook - a few grades but easily dooable if the weather permits. Strong Winds at Holdbrook on the High Dessert can be bad for blowing snow (Ground Blizzards). But if the weather is good, it should be an easy drive all the way into Alb. East of Alb. you'll do some climbing again if you go that far.
Just don't be in a hurry and enjoy the trip no matter what the weather does.
Good Luck