Brakes get hot and the rotors warp. They then cause that shake felt through the steering wheel at low speeds when lightly riding the brakes.
So that sounds legit.
If the pulsing happens while off the brakes or at higher speeds, it most likely is a tire balance issue or at worse a bent wheel or damaged tire.
If it only does it as you come down from speed, in a slower range as you lightly ride the brakes, then it is rotors. Not a real big deal. If you brake hard, repeatedly, sometimes it will go away oddly enough. Other times, if you "drag" the brake, lightly using them repeatedly like coming down a grade, it can get worse as the rotor heats and warps more.
The grinding, not sure. Is it "heavy and Metallic" feeling, like something in the steering rack or column, or light and gritty feeling like sand or dust in the steering column up top by where the ignition key is?
Since it is dark and probably damn cold out, and not a situation where you can go out and put the front of the truck up on jack stands to play with it, a quick and easy thing would be to go and do several full-lock turns right to left, like in a tight Figure 8. Sometimes the spinning of the steering wheel back and forth all the way to lock in each direction will shake out the dust, lube the shaft and rack and give you a better idea of where it is coming from.