I'm sort of torn between:
Yes, by analogy to parks.
Cities obviously subsidize city parks, and it would be hard to say that cities aren't better off because of it. Of course, those are right there where the people are, and -- at least for the traditional ones -- the benefits are pretty general to the whole population. Although ... the subsidized city parks in most places include a bunch of recreatational facilities that have (like skiing) a little more "nichey" appeal: sports fields, climbing walls, bicycle velodromes ....
Then there are the National Parks. Of course, the latest trend is to make these "self-supporting" with user fees. BUT, anyone who has a vague understanding of business and finance knows they're not remotely "self-supporting" in any real sense, because the enormous capital (all that land) isn't taken into account. You could make the argument that maintaining the park lands undeveloped is a given, and a separate "activity" from the use of the parks, and that one should thous account for the use of the parks independently of the capital investment in the land.
One other thought: Isn't Winter Park actually owned by the City of Denver and administered by the city's Department of Parks (though now managed by Intrawest)? I also believe the oldest variant of what's now Summit West at Snoqualmie Pass was the "Seattle Municipal Ski Hill."
No, It's Just Subsidizing Consumption of People Who Can and Should Pay For Themselves
Not a lot of elaboration needed.
The "economic benefit" argument
is, I think, bogus. For one thing, it "proves too much." Every business generates income, jobs, makes people spend money, creates sales tax revenue, etc. By the same logic, the government should subsidize every business, including restaurants, hotels, gas stations, oil companies, real estate brokers, accountants, drug dealers .... Instead, the government does exactly the opposite of subsidizing, and taxes these businesses, either through business income taxes or with direct excise tax levies on particular businesses. Most places actually put a higher tax burden on hotels, which is completely backwards according to the "subsidize happy economic activity" theory, since they're bringing in notoriously free-spending customers and money from other parts of the country or world.
The Real World
I don't think the government really does subsidize skiing, or at least not very much. I don't know what the financial story is with those New York areas. There are some municipally-owned ski areas around, as mentioned above. Another one is Mount Ashland. When it's that local, and that small a community though, the case becomes much more similar to a city parks: there's a reasonably close identity, or at least overalp, between the group paying (city taxpayers) and the group enjoying.
As for Forest Service ski areas, the areas do pay for the land, in the form of a percentage permit fee out of their revenues. The areas buy and own all their own improvements and -- unlike national parks, but like timber companies and miners -- do at least pay some form of rent.