I ride up hills.
I am unsure whether you are asking if people ride up the particular trails you rode in Georgia, or if people ride up long hills in general. Around here (northern New England) most of what we ride starts in a river valley and heads up over the hills. There is definitely a lot of climbing, and most everybody does it on their bikes. The bikes I have seen on the trails include everything from fully rigid single speeds, hardtail XC , short travel full suspension XC, and 5" trail bikes. I began with a 30+ pound hardtail, and now my main ride is a softail single speed with a rigid fork. I do not think there is any substitute for getting out and climbing hills to improve your hill climbing technique/abilities.
From your description, it sounds like you guys had it figured out by the end of your ride. You would probably be surprised at the hills you can ride cleanly the third or fourth time you ride those trails.
Enjoy the rides,
GF