Burton Island
From Naval History and Heritage Command
The cutters on Bering Sea Patrol were much more than symbols. They assisted in the performance of many governmental functions. For the Justice Department they enforced the law, apprehended criminals, and transported floating courts. They gathered military intelligence for the Navy Department, and carried mail for the Post Office Department. For the Interior Department the cutters carried teachers to their posts, conducted sanitation inspections, and guarded timber and game. They surveyed coastlines and regional industries for the Department of Commerce and carried Public Health Service personnel to isolated villages, otherwise without medical service.
Naval History and Heritage Command
USCG Historian's Office
Naval-History.Net
Wikipedia
YouTube:
1952 US Navy film entitled "Icebreaker" shows USS Burton Island traveling from San Diego to Bering Sea.
USS Burton Island sails through the frozen McClure Strait in Canada.
Thanks to Danny252
The Current ships page will give you an idea of what years are available.
For more precise details, see the Discussion topic and the Tracker for the year in question.