How would a warm winter affect maple sap production?
This article has a clear explanation (backed up by good links) of the effects of climate change on maple sap production, including the following:

Maple trees produce the best sap on cool days preceded by freezing nights – the cold weather causes the sap in the tree to freeze, creating a low-pressure vacuum that draws more sap up from the roots. When temperatures rise the next day, the sap melts and oozes through the tree, making for easy collection. When temperatures stay abnormally warm, as they have been lately, this process does not occur.
Additionally, the warm weather causes the trees to begin to bud.  The hormones that trigger budding also decrease the sap’s sugar content and spoil its taste. This means that it takes much larger quantities of sap to boil down to a gallon of syrup.