The airport does a really good job about staying open. Unless there is a raging snowstorm, you should not have much of a problem. I'd worry more about your connecting city (unless you are going to take the non-stop flight from Atlanta on Delta).
There are not many B&Bs in Burlington (if any-I can't think of one). You tend to find those out in the rural part of the state. There are a couple inns near UVM. One is the Lang House, the other the Willard Street Inn. If it were me personally, I'd prefer to stay downtown. There are 2 big hotels there, just across Battery Street from Waterfront Park. They are the Hilton and the Marriott Courtyard.
There is a large music scene in Burlington for a town its size. Check out
Seven Days | Vermont's Independent Voice for an idea as to what is going on at any given time in town.
Have fun!