If you want to see a hockey game, winter is hockey season. There is a new rink at the University of Prince Edward Island, and other rinks in town where you can see hockey games. But you have to buy tickets in advance, and buy them quick because some games can sell out.
If you come in the winter, you can go skiing or snowboarding in Brookvale. You would have to drive there, it's outside Charlottetown. I think you can also go cross-country skiing in Victoria Park and other parts of Charlottetown. If you like skating, there is an outdoor skating rink in Victoria Park and a few indoor rinks around town. Also, in the schoolyard of Stone Park Elementary school, there is a hill where a lot of children go sledding.
Equipment: If you don't have ski or snowboarding equipment, you can rent it at Brookvale. I think you can rent skates at the indoor rinks, but you need your own for the outdoor rink. There is a second-hand sports store on University Avenue if you want to buy cheap equipment.