Haha, yes. Well horse drawn sleighs do exist.
There is an American prisoner wagon called a growler but that has wheels.
You can get covered sleighs that a couple of people can fit in, but a friend of a driving buddy was once transported by open sleigh with a prison officer sat next to him through the night from one gulag to another and on chatting with my driving buddy we came to the conclusion that this is the most probable solution.
So an open topped sleigh with a guard in with your prisoners (probably sitting next to/near the driver), especially as if they tried to escape they would get caught pretty much immediately due to the snow and probably being manacled. It is a fantastic way to travel and those sorts of sleigh are usually pulled by sturdy hairy pony types (think mongol horses). Hope that has helped