I generally don't let anyone ride my horses. Dora is just too squirrely and unless the person is someone that I know is an experienced rider, I don't let anyone on her. I do let people ride Freckles occasionally, but as odd as it sounds, it's usually people that have never been on a horse in their life. It's like, I remember the days being younger and just wanting to sit on a horse...well, he's that horse to others. He won't do anything but plod around anyway and these people aren't looking to really "ride". They just want to say they sat on a horse. No one rides Kid but my hubby. He will throw you to kingdom come with no warning at all, but DH knows his quirks and can tell when a buck is coming and head it off.
Anyhow, aside from that, I really have no rules when it comes to dress. I ride barefoot a lot myself, but I also ride bareback a majority of the time when it's warm. I know it's still dangerous, but I've always done it and it's a risk I take. When I ride with a saddle I generally wear boots, but I don't require it of others.