That depends on the conditions in the trunk. It may regrow.

Well its hard to say at this point because, although you did take many precautions to protect them, in a zone 7/6 climate (depending on what part of NJ you are in, Windmill palms don't need as much protection as a 5/4 climate. Although we did have a tough winter this year, they probably would have been fine without the light. A good trunk wrap and some Christmas lights would have been fine. What I would do at this point is try to preserve any green left on the plant by spraying it with fungicide. also try to keep moisture out of the spear area as it may rot the bud. make sure the palm gets water from the roots and protect the crown with burlap if temps go below 10F. If all of that fails, chuck the condition of the trunk, If it is mushy down to the base its a gonner, but if not cut the top of the trunk off and it should regrow much like and elephant ear or banana. I am happy to see that people in the area are interested in T.fortunei as much as I am. Hope your palm survives
-Dave
P.S we should have a much milder winter next year :)