My experience in the case I mentioned above was the opposite: I really needed to loosen my heads for the outdoor gig, as they sounded too high-pitched and ringy -- yet they sounded nice and warm inside at the same tuning.
That's because as Diddle suggested, the lower frequencies and natural resonance of the drums were being gobbled up. In reality, there was no box (room) for the drums to resonate in and bounce back to your ears.
Having played outdoor gigs, I generally tune for the music and assume the PA will capture the resonance of the drums. My drum tech would tune the kit to my liking, not the different spaces we played in.
Having said that, I would use experience to moderate my drum set-up ideas.
I would rarely set-up highly resonant toms and undamped bass drum for a series of cavernous venues where the drum sound would ring on forever. Likewise, I wouldn't apply tape and blankets to a kit I was going to take to football stadia across America, as even with monitors you'd feel like you were playing cardboard boxes on stage.
