As erb said, sounds like you have never been to SXM. Orient is lined with beach bars, most of which have drink service at your chair. As far as bringing your own cooler, most of those beach bars don't want you to bring your own cooler, since they sell drinks. The former Club Orient beach is the exception to that, as many or most people who go to that section will bring their own coolers, with a couple drinks, or even food.
As far as walking, it sounds like perhaps you are not planning to rent a car? I do hope you are going to rent a car, as while Orient Beach is great, there is a whole lot more to see on the island than just Orient.
If you have other questions, please feel free to post here.