We have stayed offsite before and the parking lots are opened at least an hour before the parks open. I think I just read in the UG that they are open two hours prior to park openings, but even the week between Christmas and New Years, we didn't arrive there that early. Our goal was always to get to the parking lot 45 minutes prior to the park opening, sometimes we got there earlier, sometimes we got there a little later. That gave us plenty of time to get through security and be waiting for the official entry into the park. The one park that takes the longest to get to from the parking lots is MK because you either take the boat or monorail over, so you may want to plan that one on the early side. Remember to try to work around EMH, it is very discouraging to see other people walk right into the park while you are being held back. By the time you get into the park the best rides will have lines.
Good Luck.
Amy