Might be that a squadron was in Canada at some point after 1812 - may be 1813? Sure Mr DE Graves would know!

The Nineteenth and Their Times: Being an Account of the Four Cavalry ... By John Biddulph

http://books.google.co.uk/books?id=fD82AAAAMAAJ

British Generals in the War of 1812: High Command in the Canadas By Wesley B. Turner

http://books.google.co.uk/books?id=64cQcHe013QC

Ant