Ok, interesting clip after all. As Vince reported, the Jetblue aircraft did not skid off the runway. Rather, the aircraft slid off a taxiway as it was exiting the runway.
Here is the taxi diagram and an annotation indicating the approximate location of the aircraft where it became stuck in the snow and ice:
The clip starts off with (coincidentally) another pilot asking for the weather forecast, then immediately picks up with the JBU check-in. Clip ends with the USAirways aircraft accepting his clearance back to Pittsburgh.
Clip has been edited for time and some (but not a lot) of non-essential comms.