The assumtion is that they were due to the harshness of the winter.
It's a clear cut assumption, and stands in direct parallel to the criticism of the French for their perceived failings in the face of the heatwave. Without LIU exhaustively, I will nevertheless bet a guinea to a groat that the French death toll in similar fashion will not reveal the exact proximate cause of death. I doubt if anyone was killed by "fried brain pan" or whatever the medics' Latin translation is - but the overall effects of the heatwave were to cause the deaths of several thousands of people who can be expected to have lived through a more typical summer. In similar fashion were felt the effects of a severe winter in the UK; and I have little doubt that the USA stats do not show the full causal picture either.
But when an elephant falls in your deckchair, it's not much good discussing from whence it was exfenestrated. ;)
