Are they sturdy? Yes, the larger horses are very sturdy and hold up well to heavy playing (we've had them run around on concrete for years now and they haven't broken yet)

Do they tip over easily when your Doll is "riding"? yes, they hold up very well because we've managed to have up to four dolls all riding one horse before and it's stayed upright. However "sparks flying" (Kaya's smaller horse) is extremely tippy and I can never get her to stay put.

Do the dolls stay on pretty well? If you put them on in a proper riding position they stay on very well, even if the stirrups aren't on. It helps to balance it by having them hold the reigns between their fingers.

Is the horse heavy? The horse is fairly heavy, but not too heavy for younger girls to carry around.

Is it just flocked hard plastic, or is there some stuffing there too for a more huggable feel? The horse is not huggable at all, but fun to groom.

Hope this helps!
Greta