The train in High Park is pretty low-key. As long as you can fit the stroller on, I think it would be fine. We always bring our Quest and have never had a problem. I think a BJCM folded would fit, especially, since you are going to be there during a weekday when it is less crowded than on the weekends so you don't have to worry about it taking up space on a crowded train.
Yes, the weather is probably milder here than you are used to. It does change significantly from day to day. It can get hot and humid but not typically in June. It's usually the mid 20's celcius.
DS - 10
DD - 8
Twin Girls - 6