My experience and dictionary has "cosy" as British and "cozy" as US. I think recent wider exposure to original materials from round the world is making us far more acceptant of variant spellings, and variant word usage in general. This then leads to ambivalence in our own usage. We sometimes impose as individuals specific difference in our own usage; who knows why. These differences are sometimes more general (e.g. program in UK is for computers; programme is a sequence of events).
Rod
PS I just noticed that Enigma wanted Ukraine for UK!!!! Which reminds me that when my nephew applied to US colleges for a PhD., he had to satisfy the English language criteria. Being British, he was accepted by most establishments, except one. When they were asked by phone what the problem was, they replied that the country (prounounced as) "Uck" wasn't on their exempt list.