Yes you are
Yes, we brought snacks and water bottles.
Yes. The parking lot is not so large that, if you get there early, you can walk to your car and get your lunch, without the need for a locker, and eat upstairs in the lodge. Unlike some resorts where you have a long shuttle ride to-and-from the parking lot.
Yes, coolers for food and drinks are acceptable (you will not be the only one I assure you) and storage space for them is available in the upstairs level of the lodge. There are various food and drinks available for purchase as well if you forget something.
Yes. There is a very large open dining hall upstairs with tons of tables and chairs. Some people bring coolers and leave them up there on racks. They also have small one use lockers($1) and larger all day lockers ($5 and an ID). The cafeteria has food that is reasonably priced (~$10 per person) given the fact that is at a ski resort.
Yes!
Yes! I always bring a backpack with snacks and water and you can eat there
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