Skiing is expensive, I agree. But less so if you own the equipment. The same goes for a range of other activities.
Mountain biking is probably one of the best value-for-money winter sports I can think of in the UK (where I live) and NZ (where I'm from). One reasonably large expense up-front followed by low-cost or free access to various trails in various parks, and reasonably low equipment maintenance costs.
Hiking is another alternative. Though it's not really something to look forward to in winter specifically; and if you can't enjoy it in summer, you probably won't in winter. Slightly lower up-front costs (some microfleece clothes and a good waterproof coat and hiking boots) but even lower transport costs.
Of course both of those still come with a transport cost. If you need to avoid that as well, you should consider photography. I've found that since I've started developing some photography skills I'm never too sad about the climate- there's always something outside to try and capture nicely. And if you're able to throw in some hiking (or even walks in parks nearby) it becomes much nicer. The current season is especially fun in the UK where most of the trees (those that I've seen) are deciduous, unlike NZ.
In any case, you may have to put some effort into any of these things; I didn't really enjoy winter hiking to begin with, but I've learned to really enjoy it. And, to be clear: not begrudgingly. Very enthusiastically.