Is there an accepted standard for storing data as a year?
You can achieve this in Webform by hiding the day and month fields as well as deselecting the enable pop-up calendar option on the webform component.  There you can also set how far back you'd like the years to go.

However, Civi still stores the entire date.  I believe the date will be stored as Today's date, 2015 12:00 am if you select 2015 for example.