As others have stated, this depends to a great degree on your location. If you are in Canada, access to hockey leagues and ice is fairly easy. Paying for it is another thing entirely. I played hockey using the same strategy that Pio mentioned with hand-me-downs and used stuff from sales. But it was still expensive. Nowadays, it is almost prohibitively so. If you think of a kid in hockey from age 5 to 15, think of how much they will grow. You need new (or new used) equipment every year. If you add in the cost of travel to a few tournaments a year it is expensive. Usually a minimum cost of around $2500-$3000 per year. No way around it.
Curling is cheap. Relatively. Join a league, get a broom and one of the sliding things that goes over your shoe and you are done.
Cross country skiing is reasonably affordable. There is plenty of used equipment around and it costs nothing to go out to the woods somewhere to ski.
Downhill skiing is more expensive, and the cost of it is probably the most dependent on location. If you are in a location where you can get a season's pass and use it all winter long, not that bad. If not, travel and accomodations get expensive. Ski equipment can be had for reasonably cheap, and there is lots of used equipment around.
Now, so far I am just talking about these sports in the context of recreational enjoyment, not serious athletic pursuit. To do that, all sports require coaching which gets expensive. You will likely need to make a provincial or state team for whatever it is you are pursuing. This will costs LOTS of money as there will likely be extensive travelling. Yes there is financing for some portion of the cost, but most is going to be borne by the athlete until you get to the truly elite (ie. national) levels.
Speed skating only requires a pair of skates. But add in the coaching necessary to get good enough to get to the elite levels, and the travel time to succeed in getting to the elite levels and you once again have a very expensive sport.
I suppose the crux of what I am saying is that these sports can be done recreationally in a reasonably frugal manner, but anything more serious than that, in any sport, is going to be expensive. Add in the locational aspect of some winter sports and high level success in these winter sports is very expensive. But so are a lot of non-winter sports. Soccer is often touted as the prototypical cheap sport. Maybe in third world countries, but in North America if you want to be good it will be expensive. My brother-in-law's niece is a very, very good high school soccer player (plays on the provincial team), cost is around $10-12,000 per year.
Success is expensive. Recreation not as much. But it ain't cheap.