I have another lesson this evening :) I ride a horse :) He's a big gelding, around 16hh (I don't know the exact measurement; I'll compare him to the horses I know are 16.1hh and 15.3hh xD) and of a mix of breeds but definitely some cob as he's got a huge bum and is stocky and chunky. I'm tall with long legs (I'm five foot eight and my legs are longer than those of a six foot two male friend) and I've ridden something that was about 13hh and it was the most uncomfortable ride I've ever been on!
I definitely like big horses. Longer stride, so you don't feel like you're sitting on a jackhammer, and you're just so much more secure! On the pony, at first I felt like I was about to come off in trot (I ended up shortening my stirrups to rectify that, though), but I've never once felt off balance or about to fall on Charlie Brown, even with really messy trot/canter transitions.