I've double towed up that with a 25 foot 5er and a 14 foot flatbed with 2 utility quads on it. It has about a 6 -7% grade in a couple of places and one 150 degree turn near the top but its not too tight. The 5er has gone up that several times. There is a short tunnel but it has plenty of clearance. You shouldn't have any trouble.
Going east from Cloudcroft to Artesia doesn't have anything to worry about.
When you get to Cloudcroft the Western Cafe is a good place to eat. It's on the tourist trap street a block north of the highway.