Yesterday, I was helping a friend of mine move to a different house, and I had my truck all loaded up. I got in and took off, but I never pushed the "Tow/Haul" button on the shifter. After driving a ways, I noticed that the truck seemed to be shifting like it was in tow haul mode, and when I looked at the instrument cluster, the "Tow/Haul" light was on. I guess it came on automatically. Is this normal? When I unloaded it and restarted the truck, the light did not come back on.

Sure someone didn't hit it for you after you started up or you bumped it without noticing when you backed up?

Nope, I asked my friend who was riding with me i he had pushed it, and he didn't. I know i didn't come close to the button, either.

Transmissions in newer trucks will do this when they get to hot. It is a safety to keep you from overheating your trans.

The truck had been sitting for an hour after only driving ~3 miles unloaded

However it got turned on in the first place, at least you it went off. Driving in tow/haul mode for too long will use up a lot of gas. It automatically turns itself off when the engine shuts off.