As far back as 1793 the volunteers of New York City had sleds built to help respond through the snow filled streets. In that year, because of heavy snow the December before, sleds were built for Engine Companies 17, 18, and 19. (19 even was allowed 2 additional members to help pull the rig- due to their longer responses.)
The cool picture of Black Joke Engine 33, shows their goose-neck pumper fitted with “runners” for hauling the machines through heavy snow. The other picture shows E-33 on the deck of a ship at the foot of Wall Street during the Great Fire of 1835. They were relaying water from a patch of open river to other pumpers on shore. Remember, all pumping then was done by hand!
* I have found no other mentions of the paid FDNY of using sleighs except the below photograph.