Does the Highway Traffic Act include laws for frozen lakes?Any public "thoroughfare" were a vehicle can access (shopping malls, underground parking in residential condos, etc.) is subject to the highway traffic act. I once asked the Owen Sound prosecutor if I could get nailed for Impairdo on my cottage road which is a "Private Road". I asked because I use to take my ATV down the road visiting fellow cottagers with my "mini bar" on the back since I'm very particular about ice cube quality.

Now I walk. Not nearly as much fun.

Even though this cottage road is private property, it's still open to public thoroughfare. Residents, their friends, tradesmen and the Police all use it. Hence it is a "public thoroughfare" according to the Highway Traffic act.
If the lake is not privately owned and it is used by snowmobilers and other "motor vehicles" then it's a "public thoroughfare".