Here is the parking page on Disney’s website:
Standard overnight self-parking is available to registered Guests for a fee that will be applied to their hotel folio upon check-out. All parking fees include applicable tax.
Complimentary standard parking is available to Guests staying at the Campsites at Disney’s Fort Wilderness Resort. Each campsite provides parking space for one (1) motorized vehicle.
Standard theme park parking is included for registered Guests of Disney Resort hotels and select Annual Passholders. These Guests can also choose to enjoy preferred parking by paying the difference in cost between their included standard parking and preferred parking (difference is currently $20-$25 per day*).
I also found this relevant tidbit on another site:
Guests at the campsite receive free parking for one motorized vehicle; additional vehicles and parking at the cabins are subject to Disney’s regular parking fees.
To summarize: If you have a reservation at the campground, you will get one vehicle parked at the campsite AND the parks for free. You will have to pay for each additional vehicle at a single campsite, but those guests will not have to pay for parking at the theme parks if they are registered guests at the campground.