They specifically state that certain items can be kept in vehicles, but the language isn't present following the prohibition on weapons, which implies they are prohibiting weapons entirely on the property, including the parking lot.
"Cans, canteens, glass containers, glass bottles, or coolers are not permitted on site (inside or outside) at the Ark Encounter but may be stored in vehicles."
That's an issue for them and they should word it better to expressly permit weapons in vehicles.