I do not think the British ever used Carden-Loyd tankettes to pull ski-troops, yet I have seen Canadian, Swedish, and Polish (TK) Carden-Loyds used in this role.
It is interesting that all three countries developed this practice indepentently. In this role the tankette would be a true infantry-support vehicle. Compare this to how a lot of tankettes were expected to fulfill the role of the light-tank! The ski-troop towing seems much more in line with the capabilities of these vehicles.
I posted this, because I happened upon this Ebay auction. The item is a picture of the rare Carden-Loyd MK.VI built for Canada, towing ski-troops.