Parking is most definately free once you enter the Conwy jurisdiction.
It may be a few hundred yards extra to walk, but you can park safely all day, safe in the knowledge that no nasty yellow plastic bag will be on your windscreen if you out stay your welcome.
Why the rules for Gwynedd are different from Conwy, i have no idea, as its a backward step, booking tourists who may never return to the area, after having a parking fine.