It's due to weird character motivation. Riker originally seemed like a 'cowboy' so naturally he sit down by swingin' his leg over the saddle. This didn't really jive with the character development though, so it seems unnatural. I think Picard is the only one we see riding in TNG - although in one of the books I read recently, Riker claims to have 'ridden a variety of animals from different planets' which is DEFINITELY a claim you can prove with canon.
I sit like this pretty often; thanks for making me self-conscious!