Mechanical Horse: While recognizing the general principle of the occasional usefulness of walkers, the Imperials generally prefer mechanical spiders, or at least hexapods. Extra stability is always nice.
(They’re also not generally used for military applications [but see also Spider Tank]. The legs, and the joints in particular, are just too vulnerable.)
Spider Tank: The classic eight-legged war walker is mostly averted these days, thanks to vector control and modern power reactors letting you build hovering tanks, with rather lower maintenance requirements and fewer vulnerable joints, but it was quite the staple back in the day. (Not to replace regular tanks, which had large maintenance and vulnerability advantages where the terrain suited them, I hasten to add, but to operate in places where regular tanks couldn’t go.)
And their smaller cousins are still around, as fighting drones, which usually come in swarms of little spidery drones, all fully equipped for wall-climbing, cable-spinning, and duct-navigating.