Parking (as far as mothballed parks go as a whole) will probably depend on where people are parking and if it's legal or not.
The whole point of mothballing parks is that they stop using any Ranger time which costs money. So if people are parked on State Parks property, no Park Rangers are going to go there and ticket them. I am not sure if local law enforcement would have authority to do so, that's something to discuss with your local rangers.
But I bet at many of the parks, they'll block them off close to the main access point, so if there is no parking on the public roads outside the park, people are going to have to get creative.
There's no easy solution in most of those cases. But good luck at Peshastin, I hope you all are able to organize and find a solution that still gives you climbing access.