The Air Force got into running around 2003, and fitness is a much bigger part of the culture than it used to be.
I can get you a definitive answer about Ft Hood in a few months when my son gets there. He's a TACP officer, so he will probably be in your old unit. (They renamed the career field a few tears ago.)
I was in the Air Force thru 2008. Running was pushed but there was no formation morning runs - unlike the Army, who would jog past our Detachment in formation first thing every morning.
Around 1990, our squadron had its annual fitness test with 1.5 mile run. They shut down the runway and had us run down it. At the finish line was enough cold beer for half the squadron! A number of us ran pretty good that year....
;>)