Usually Meziadin and Boya Lake close after the first snow fall. They don't have a way of clearing the snow so they close. Unless the provincial gov't has set a firm date now to save $$. The BC Parks website indicates Boya Lake closes on first snow fall but may not have firewood or services after Sept 26.
In Yukon, the territorial government campgrounds vary with their closing dates. It seems to depend on the contractor caring for the campground, and on the first snow. It also depends on how active the bears in the area might be as they feed up for winter. Congdon Creek campground on the shores of Kluane Lake often closes early in the season due to a local grizzly feasting on soapberries around the campground.
The private RV parks are variable too. Some highway lodges and RV parks close immediately after Labour Day, because the owners also want to head south. Usually the businesses owned by locals remain open through September to catch the business from the Alaska RVers heading south. A park owner in Haines Junction told me she gets most of her business in September and early October with the southbound folks.
Some are getting ready to close in September so may have already blown their water lines out but can let you fill the tanks at a communal water tap.
We often travelled from Vancouver Island to Yukon in late August and September. Never had a problem finding campgrounds, other than the one trip southbound between Fort Nelson and Dawson Creek. Everything was full with gas & oil field workers living in their RVs at the campgrounds. We eventually pulled into a rest area and slept.