I would tend to suspect brakes or wheel bearings.
I think you have front disks.
If a wheel bearing gets loose, it will rub on a brake pad or part of the truck, but usually run true for a little while when you center it by hitting the brakes.
Also, you could have a problem with a pad.
Should be easy to spot, just jack the front end up and spin the tires.
NOTE: You might want to do this right away.
I had the same noise after doing some tree moving in my truck. It did not change when I hit the brakes, and was faint enough for me to ignore until I had time.
I figured I had a branch caught somewhere.
That afternoon, I had to hit the brakes hard to dodge a dog, and lost all front brakes.
Turned out that I had bent the metal part of the front hose where it went into the front caliper, (it was a Ford) and the rubber part was rubbing on the inside of the tire.
Finally wore far enough through that it blew out.
