Hello. Started sound like broken record here, solved one problem and find some new.
Truck has some nasty vibrations when driving +40 mph. It get better when speed gets over 50 mph, over 60 hard to tell does it still shake or vibrated.
Some times no shaking just vibrating and after driving 20 miles it get little easier. Truck shake/vibrated more when cold.
I have replace driveshaft u-joints, carrierbearing, did not do anything. I did replace brake pads ans discs front and rear + one leaking brake caliper. This helped a lot, shake went away but still vibrate while driving over 40mph.
I do have new u-joints in front end and locking hubs also and front hubs+bearings are 2 years old.
I will change my tires to summer brand when it get little warmer and no more icy roads in early mornings. If tires wont be answer what it could be? shocks?

 

Other than a general suspension inspection, I would balance and rotate the tires.

Shocks? Maybe... Not so much directly, but weak shocks can result in tires cupping. Cupping will not really balance out, but rotation will minimize it. Cupping can often be seen as alternating gray and black patches on the tire treads, and is more likely on the steer tires.

 

Check for a frozen caliper/blocked hose. My F250 did something similar when the last one failed intermittently, at first. It was pretty easy to isolate, just stop and hold your hand near each of the wheels immediately after observing the symptoms. The faulty wheel will be very hot compared to the ones that are okay.

 

Ok my 04 had the same vibration, started around 45 through 70ish then smoothed out around 80mph. I chased it for over FOUR YEARS! I finally gave up and took my factory aluminum wheels off and put ford OEM steel work truck wheels on the same tires I was running...TRUCK IS SMOOTH AS SILK
Shop had a 1" thick machined block of steel and when you keyed my aluminum wheels on it two were perfectly flat the other two had a wobble in them...for some reason two got out of round. Shop told me most likely tire changing machine did it years ago

 

What is the difference between a vibration and shaking?