To answer your question: No, it isn't "normal" not to have a reception.
Many posters have offered suggestions on alternatives to a formal reception:
1. Have a dessert party. With site rentals from $200-350, and menus starting at $25/person it is very reasonable. Plus, it seems as though all your guests will have theme park admission, so no Illuminations viewing fee.
2. Have dinner at a buffet onsite. Again, it would be about $30-35/person. Very reasonable.
There are a lot of risks with "winging it" as you hope to do. First, large party dining reservations are typically only offered at the 1st and last seatings. So your choices are going to be 5pm and 9pm. I'm not sure, logistically, how everyone will pay for themselves, as you suggested. Split the bill 8 ways?
If your groom is in a tux, or even a full suit, you will not be allowed to enter the park. And even if your dress is casual by "bridal" standards, the odds are you will not be permitted to enter.
And as far as asking family and close friends to a destination wedding and not providing them with a meal...in my opinion that is a bit tacky.
These people will be paying hundreds of dollars, maybe even thousands, each to travel to and attend your wedding. I'm not saying they should be given a 7 course meal at Victoria & Albert's, but a meal/experience costing $25-35/person seems more than acceptable to me.