Winter is an odd season since its weather spans calendar years.
Winter time in 2015 would include the months of January, February, and December for the calendar year in 2015, based on the alignment of Memorial Day being the beginning of Summer (June, July, August) and Labor Day being the beginning of Fall (September, October, November).
However, Winter is a season.
From my experience (and possible bias), Winter 2015 refers to December 2015, January and February 2016. Christmas and school holidays being the anchor for what is "Winter".
Often, "January" and "February" in the Winter season gets referred to by name: January 2016 (Winter 2015).