dressage

[tiny tim]

Which same word can be a bounding movement of a horse during dressage and also a support for the rider's foot which is attached to the saddle?

[icemaiden]

well stirrups or irons are where your feet go into and they are attached to the saddle. But I have not heard a dressage movement called either of those.

[icemaiden]

unless its a western saddle, which would make it a "Fender"

[boodle]

sturrups unless western in which case fender (SOZ CANT SPELL)