can·ter / ˈkantər/ • n. [in sing.] a three-beat gait of a horse or other quadruped between a trot and a gallop: I rode away at a canter. ∎  a ride on a horse at such a speed.• v. [intr.] (of a horse) move at a canter in a particular direction: they cantered down into the village. ∎  [tr.] make (a horse) move at a canter.

canter a pace of a horse between a trot and a gallop, with not less than one foot on the ground at any time. The word is recorded from the early 18th century (as a verb), and is short for Canterbury pace or Canterbury gallop (see Canterbury).
at a canter without much effort, easily. A horse-racing metaphor, implying that the horse has to make so little effort that it can win at the easy pace of a canter rather than having to gallop.

canter XVIII. Short for Canterbury gallop, pace, trot (XVII), a pace such as mounted pilgrims to Canterbury were supposed to have ridden.
Hence as vb. XVIII.