If you want to stay low, see if there are horses that does not go up and down.
If all of the horses in a row are occupied, the weight balances out. But if all the horses in a row are occupied by really heavy people, I cannot rule out having that portion of the mechanism and framework disintegrating. The carousel at Slater Park in Pawtucket RI is one of just a few where none of the horses go up and down.
The very first carousel ride I can remember, I specifically wanted a horse that did not go up and down as I was afraid of heights. I was too young to tell my father so but (I think) I kept pointing at the horse I wanted. My father finally moved me to the horse I wanted.
I am so glad I'm not the only one to have trouble getting off the thing! I don't even use the stirrups any more, just kind of slide down on my belly. I'm not even that short or fat, just uncoordinated! It is sooooo worth the humiliation though - I love riding the carousel. It will make you feel ten years old. 
