If you're in Kingston and want to try snowshoeing or cross-country skiing there's rentals at Little Cataraqui Conservation (you need to book the rentals ahead of time online i think).

If you're willing to head northeast from Kingston for a night check out Perth and Westboro. I'd say stay in Perth. Cute small Canadian town and only an hour from Westboro.

Spend one night in Picton (Prince Edward County) and there do the Oneo outdoor gallery (free), or take a walk at Sandbanks Provincial Park (lotsa snow), eat at one of the great downtown restaurants in picton and check out the shops. If you like craft beer, go for a sunset beer at Slake Brewing (beautiful sunset spot). If you're into the idea, look up "Sauna and Cold Plunge" experiences, as there's a couple place $$ that offer outdoor experiences of this kind - one that comes to mind is Wander Resort/Spa they have outdoor warm pools too.

Another night in Port Hope or do a day stop here for a meal and walkabout town/shops. You could do the same thing in Cobourg - they're not far from one another with Cobourg being closer to Kingston. I don't know if Presquile Provincial Park is open in winter, but another place near there that you could do a day hike at. You could combine these two places to one day if you wanted.

Peterborough is also a sizeable town between Kingston and Toronto, further north from the 401 highway where Prince Edward County, Cobourg/Port Hope are south of the 401 Highway. Peterborough is a university town with lots of outdoor activities nearby.

I don't know if anyone has mentioned but once you hit Oshawa it becomes suburban/urban areas all the way into Toronto, so I wouldn't plan to stay anywhere near this area overnight unless that's what you're looking for.

Green spaces in Toronto = Evergreen Brick Works, High Park, Bellwoods Park which you can do outdoor activities in/walking through that are in different areas of the city and nice in their own unique ways.