We are planning to climb Mt Huashan in December . Dec 1-5. Is it too late and too cold?

No, it’s not too late. You can still enjoy the different scenery of the mounatin in chill time. It will be very cold on the mountaintop. It will cold at that time, and the temp on the mountain top is much chiller. You need wear sweater, heavy coats, down jackets and boots.