Specifically, I'm only interested in visiting the Canadian side of Niagara Falls; hereafter, just refer to it as Horseshoe Falls. I know that the closest parking is priced, and so any free parking must be more farther from the Falls. However, where's the closest free parking?
There's free parking along the Niagara Parkway which can get you close to the the Falls, but it's a long street so that can vary as well but it's the closest you can get.
Your other options are the areas outside the central Falls and Park that also have free parking.
White Water Walk, Whirlpool Aero Car, Queenston Heights Park/Restaurant, Old Fort Erie, McFarland House (free if you're visiting the House I believe), Mackenzie Printery, Laura Secord Homestead, Floral Clock, Dufferin Islands and Niagara Glen Nature Areas, Kingsbridge Park (a parking fee is charged on weekends and Holidays only June 25 to September 5), Legends on the Niagara Golf/Clubhouse, Whirlpool Golf Course/Restaurant, Oak Hall Par 3.