I am a local resident and normally park overnight in one of the local NWDC car parks.
Can I still do this?

In most car parks the charges are only effective between certain daytime hours, so people will still be able to park in most of them for free during the night.  However, residents will need to comply with any new Parking Order, which currently means (in most cases) they will need to remove their vehicle in the morning and/or pay the relevant charge.