I visited leh , nubra valley and pangong lake a few months ago, so not December but I can tell that during December it’s not the best idea as most of the roads can be closed with possible landslides and weather impact. ( our Cab driver himself told us he has no work during the winter so I’m guessing you can’t do it in the winter ?)
safety wise - it’s very well protected with army bases being nearby.
Hope you’re not scared of the heights though
Also, as the above member said, 1 day rest once you have made a reasonable climb is recommended to get used to the lower oxygen levels being a desert area and all that.
My elder sister suffered a lot because of the above but others didn’t, someone at the hotel we stayed at needed oxygen as well, so carrying an oxygen cylinder is not a bad idea.
keep in mind, dry toilets (look it up) and only postpaid BSNL connections work there (no signal / patchy signals at many places as well).
If you want some recommendations for places to stay etc send me a pm, my brother in laws’ friend is a tour planner there, will give you his contact info.