When we go to the parks later in the afternoon, we just go around the cones and park as close to the entrance as you can. There isn't anyone directing traffic, and all the cars are doing this.
I went to EMH in Jan and arrived at the MK parking lot around 11pm. There was no one directing traffic, so I parked as close as possible. I was across from the handicapped parking area and could walk to the TTC. I'm not sure if this is always the case, but if there aren't any parking attendants, definitely try to get as close as possible.