They can't prevent you from BRINGING SNACKS, but they could prevent you from EATING THEM. Some people in the past have been asked to leave because they were eating and drinking their own food right in front of the restaurants on the beach. If you really want to do that , it is recommended that you set up your own chairs in an area away from the restaurants on Orient Beach or go to an area with no facilities like Plum Bay Or Longue Bay. The Club O area also has no problem with you bringing your own supplies for the day.I have seen people on the Anse Marcel Beach bring drinks and snacks for their children and later they all went to the restaurant to eat together later in the day. Being courteous and respecting the businesses on the beach is the key.