You know, for the riding-animals-thing, I honestly imagine...that Katara and Sokka sat it out. Like, they just stood on the sidelines and went, "Uhh...thanks, but no thanks, Aang. You have fun, though! We'll stay right here (where it's safe) and watch out for you!"

I imagine that one of the keys to riding animals (especially those that do not want to be ridden) is, well...surely agility, coupled with a strong, firm hand/grip. Aang, in his training as an airbender, has those...while Katara and Sokka do not.

But that's just what I imagine.