Hmm, interesting. I've always thought that if a park is intended to be a place where you can stay a while, it will have a public restroom. Public restrooms tend to have water fountains attached. I can think of a few tiny parks near me without plumbing of any sort, but most parks near me do have these facilities. Is Toronto that different from the US in this regard?
If that fails, check other public buildings (libraries, city halls, universities, etc.). These won't be open 24/7, but at least during business hours you should be able to get inside to use the restroom and refill a water bottle.