I concede, four helmets does seem like a waste. Then again, any one helmet is going to compromise just about every usage, so there聮s an argument to be made that four helmets is the best route.
The EliosThat said, it聮s helpful to think of how the different activities you mention affect helmet usage. I think the best argument for a purpose-built helmet can be found in cycling, where it聮s easy to generate a lot of heat in a hurry. So a cycling helmet works best for that sport, something such as the Array ($100). An excellent, light, well-vented helmet.
Kayaking helmets are not unlike climbing helmets, but tend to have a foam liner that could make them hot when climbing. So maybe take a climbing helmet kayaking聴聮s Elios ($70) would do double duty nicely, in my view. It might even work for cycling, if you聮re doing sort of casual rides. And it聮s actually intended as a bit of a multi-sport helmet.
For winter, ski helmets are designed to be warm with liners and ear covers and to give you a handy place to park your goggles. Cycling helmets are definitely out. But you could don a thin stocking hat and wear the Elios, and you聮d be just fine. Otherwise, 聮s G9 ($100) gives you good skull protection at a reasonable price.