Sure; mounted warfare existed for centuries before stirrups were invented. Actually it's not entirely clear whether the Proto-Indo-Europeans actually rode the horses or just used them to pull chariots.
Did mounted warfare exist before stirrups? The bronze age was all about chariots, and had little or no mounted combat. I'm not sure if that was because of a lack of stirrups or because horses simply hadn't been bred large enough.
The big question is of course whether Alexander the Great's famous hetairoi used stirrups or not. According to [0] they're considered among the first shock cavalry, and yet I can't find anything about them using stirrups, so clearly mounted combat, including shock cavalry, must have been possible without them.
