LAST EDITED ON Mar-22-12 AT 06:33AM (MST)[p]Yeah, you can go whenever. You just have to pay the $9 to get in (I think) maybe the price has gone up. There are some campgrounds you can stay in as well.
The access is restricted to the trails and you can't pick up any sheds or anything else. The shed hunt is only ONE day for each side of the island per year.