Here is a Santa Claus figure featured in an advertisement from the Canadian Illustrated News of 1883.
Being Canadian he is, of course, equipped with snowshoes and sled.
Here is a Santa from the same magazine in 1885.
You will note how distinctive this version of the Gift Bringer is. He is clean-shaven and wears no furs; instead he had a voyageur’s ceinture flechée sash, a floppy voyageur toque, and he is pulled by six reindeer. His sleigh has no runners (which would be useful on snowy roads) but is flat-bottomed like dog-powered sleds, good for deeper snow. Among the gifts he carries are a sword and a musket.