How can I take advantage of freezing winter cold to cool my servers without exposing them to humidity?
That may be as easy as turning off the humidifier or blocking it from the room that the servers are in. If you've got a central heating system just blocking the vent(s) and returns for that and slightly opening a window will give you a slow transition. How much outside air you need depends on how many servers you have.
Note that your next problem may well be the lack of thermal insulation between the server room and the rest of the building. If the server room is at a comfy 1°C and someone in the next room is trying to stay above 10°C, the thin, uninsulated internal wall between the rooms will do little more than stop the draft.
If you just have a server rack in a room normally they are designed to be sealed off to some extent so you can can pipe cold air through them. Rigging up some ductwork from an outside window to the bottom of that rack, and more from the top back out would be the next best thing. But again, you will possibly want to insulate the rack and ducts so you're not sucking heat out of the building. With a little thought about the duct runs you should be able to keep water and snow out of the servers - mostly make sure that ducts enter the room then go up a metre or so, rather than straight to the server.
But if you are already using heat pumps to cool the server room, you're better off making sure that the hot side of the heat pumps has a good supply out cold outside air (this sounds obvious but is often not done).
Note that if you're trying to heat the building all of this will just push your heating costs up. Right now your servers are part of the heating system, so while you might want them to run cooler, doing that at the expense of losing building heat is going to cost someone money.