Hey, we went to Kasmir in December, and believe me, above all those rumours, its a perfect place for travelling considering that you plan it properly. I have posted a detailed itinerary in my trip if you wanna check it out. Have a great trip!
Italy and Spain are quite comfortable during December as the weather is not in minus. Also, the tickets are reasonably priced due to a high connectivity between Rome & Delhi and Madrid & Delhi. The Christmas markets make the atmosphere almost magical. You can also consider Bali as the weather is pretty much the same all year round and it works out to be relatively cheaper. Sri Lanka also offers a great package.