I haven't really found any info out there about the vibration or shuddering issue while towing, so thought I would throw this out there.
I just got an 05 Supercab fx4 4x4, with 5.4, 3.55 gears, and General p255/70/17 tires. Rides nice and smooth with no vibrations or shuddering, until I tow a 18 foot open trailer with a 2600 lb race car on it, then it gets a vibration. Don't matter what speed I am going, it is there, it just seems to get worse the faster the speed.
Just curious if anyone else out there has this problem only while towing. thanks

 

Maybe the weight of your trailer squatted the truck down to where it changed the pinion angle slightly? These trucks are very sensitive to driveline angle changes, that's the only thing I can think of.

 

Have you tried just towing the trailer? If so did it still shudder the same?

Towing a race car with a big Dodge, years ago and I started getting a shudder, turned out to be a brake problem on the trailer.
The shudder was still there when we had offloaded the car and I was taking the trailer to another location.
It shuddered less, but still there. That's how I figured out it was in the brakes. A spring off, but it made the whole truck and trailer shake.

Good luck
Chris

 

How are the trailer tires? May not be the truck at all if it only happens when towing that trailer. Maybe try towing something else see if the vibe is still there.

 

I have noticed the same thing when towing my trailer with atvs. it did not do that with my previous trucks. Once you get over about 65 mph it seems to smooth out. I also have a very slight vibration or more of a rough ride with out the trailer. Have you noticed any vibrations upon braking . Iwill be taking mine in soon for the braking part. One thing that seem to help with the trailer deal was i raised the height of my trailer ball to put a little rear tilt to the trailer. good luck

Cashman

 

Towed the car and trailer again over the weekend. I pumped tire pressure up on the pickup to about 50 lbs, and seemed that it took care of the vibration, hopefully that was it, and the problem is solved. Thanks for the info guys.