Do I need chains in the winter to get to the state park?

Yes if you're driving up in the Idyllwild area you'll see the signs that require chains if driving in the snow

Yes, in fact you are required to have chains with you, snow or no snow, during the winter. We didn't find out about this until we were there. Fortunately it wasn't a problem.

Yes

Yes if you going through the back side but as of right now no snow