Quick answer: No. There was no British cavalry in North America during the French & Indian War. Of course there was British cavalry with the Allied army in Europe during the Seven Years War, which was the same war on the old continent.
Slightly more complicated answer: There were very small numbers of Provincial mounted troops here and there in British North America.
There were a dozen or so Virginia Light Horse scouting for Braddock's army in 1754. Best guess is that they were dressed similarly to other Virginia Provincials at that time, blue coats faced red, it's hard to say how they were armed.
There were a couple of dozen mounted Georgia Rangers who patrolled that colony's frontiers. Officially they had a blue dragoon style uniform with broadswords and pistols, but I suspect they wore frontier clothing and carried muskets and pistols when on patrol.
Without looking anything up...some of the more established colonies like Massachusetts and New York may had a fancy-dress troop or two of militia cavalry to escort the governor on parades. I think the Philadelphia Light Horse Troop of the Pennsylvania Associators dates to the F&IW. These units didn't serve on campaign in the F&IW, but might theoretically have been called out if a French invasion fleet had ever hove to in Boston harbor.
I can't recall specifics, but I expect that small numbers of mounted provincials served as scouts and couriers wherever the war was active.
