The name used among the people of Bree for the tenth month of the year, which would have started in late September and then run on through most of October on a modern calendar. The name derived from Old English wintrig, referring to the onset of winter as autumn began to come to a close.
The name of this month varied from the usage in the Shire, where it was called Winterfilth. The inhabitants of Bree drew some amusement from the 'filth' part of this name2 (though in fact it came from an old word for 'fulfilling', and had no connection to 'filth' in its modern sense). For the ancient Hobbits, the month of Wintring or Winterfilth had at one time marked the end of one year and the beginning of the next (that is, the 'fulfilling' of the year), until they came to adapt their calendar to the Kings' Reckoning of the Dúnedain. According to the Shire-hobbits, at least, the form Winterfilth was the original, and Wintring was a later variation devised for use in Bree.
Notes
1
Wintring was by no means the most 'wintry' of months on the Bree calendar (that would have been Yulemath or Frery, approximately December or January on a modern calendar). In context, the name must have meant something like the 'coming of winter', so Wintring marked the beginning of the colder months of the year, rather than the most 'wintry'.
2
Both the names Wintring and Winterfilth are Anglo-Saxon words adopted by Tolkien to represent the ancestral tongue of the Hobbits, who would actually have used quite different names, though presumably with related meanings. We must assume that there was some equivalent in the Common Speech for the 'filth' in Winterfilth that caused such amusement in Bree.