Beignets is a GREAT suggestion, as are pralines and shaped chocolates. Blue Frog Chocolates is a popular New Orleans chocolaterie, and they make choclates shaped like crawfish, gators, fleur de lis etc. They also do chocolate dipped Zapp’s, which would be a unique dessert bar item. I would suggest checking out their site for other great ideas. If you do not want to order all the way from NOLA, you can no doubt find a dessert place near you that can make similar items.
Of course, there needs to be a king cake. You could do multiple varieties of king cakes, from plain to different fillings, which would fill up a good portion of your dessert bar. It would be a cute option, like those who do different types of pie or different varieties of cheesecake for their dessert.
Bread pudding is a New Orleans desert staple, and would look adorable in little mini ramekins. You could also do Hubig’s Pies. Moon pies are a popular throw at Mardi Gras parades, so would be a cute touch.
Angelo Brocato is an old, VERY popular New Orleans bakery, and their packaged biscotti are sold everywhere. It is an Italian bakery, however, so it may go a bit off thme for you. NOLA locals would recognize it as a New Orleans food, but others may not see the connection.
You could do cupcakes in Mardi Gras or Saints colors, or with little chocolates fleur de lis on top. Also, frosted sugar cookies, shaped like fleur de lis or mardi gras masks etc.
While snowballs would be AMAZING, and you can actually affordably rent snowball machines for weddings near New Orleans, I doubt you can find one near CT. There’s probably just sno-cones around there, which is entirely different.
You could add a coffee station to the end of your desert bar, with chicory coffee.