There's a good number of county forests west of Toronto. If you take a look at the Grand River Conseration Authority website, they show several dozen such areas that can be hunted for a $40 fee per season for those with OFAH membership/insurance. I think it safe to say that it's predominantly cottontails in the southern portions and snowshoes further north around Luther Marsh. There are also some county forests south of the 401 and West of Hwy 6 around Valens Lake and Beverly Swamp (a good spot for rabbits and open to hunting), though the neatly planted county forests tend to hold less game.
Along with a friend of mine at Beverly Swamp we flushed a bunch of rabbits without a dog several years ago and it was noon/mid-afternoon. It seems as though the overcast weather or the fact that a storm was approching brought out the rabbits through the middle part of the day. The rabbits were cottontails, and it was only my horrible shooting that let them get away!
While I am at it, there's alot of county forests in Simcoe County north of Toronto (do a web search for Simcoe County Forests), though many of them are mature stands .Nevertheless they might account for a grouse or rabbit, and a few have mixed habitat. The Copeland forest would be another good bet off Hwy 400, with grouse and waterfowl as well.
I cannot speak for the county forests east of Toronto, since I've only seen them on maps, though I saw a number of rabbits driving around Brighton Wildlife Management Area off the 401 two years ago, but alas it's 2hrs away.
Any open bored 12 or 20 ga should work well in any of these areas.
Regards,
Frank