For the adjective meaning made of wool, woolen is the preferred spelling in American English, though woollen appears about a tenth of the time. In the main varieties of English from outside North America, woollen prevails by a large margin. Both spellings are common in Canadian writing.
Woollen is by far the older spelling. The OED lists examples from as long ago as the 15th century (descended from Old English sources). Woolen first appears in the 16th or 17th century, but it was rare until Americans adopted it in the late 18th century.
Wool is increasingly used as an adjective in place of both woolen and woollen, and this probably explains the recent decline of both those forms, as shown in the graphs below.
Against the cold and high wind, they wore old woolen caps and weathered team jackets … [New York Times]
I’m leaving the Timberland boots at home next month, along with the fleece parka, the woolen hat, and the lined leather gloves. [Boston Globe]
Mr. Bouchard, the captain, wore a woolen hockey sweater in the famous red-white-and-blue livery of the Canadiens. [Washington Post]
Outside North America
His face was covered with a blue woollen hat and striped scarf and he spoke with a local accent. [BBC News]
The green woollen background is topped with woollen representations of a daffodil, a crocus, a rose and other flowers. [Irish Times]
The ethereal woollen gown worn by Tilda Swinton is one of the original costumes from the film trilogy … [The Australian]
This ngram graphs the use of woolen and woollen in American books and magazines published from 1800 to 2000:
And this ngram shows the same in British sources: