"I have a photo taken in July of the temperatures - they post them. The overnight low was -99.9 celsius. . . ."

Not possible - the gauge must have been malfunctioning, or they just simply posted the wrong temp. The coldest temperature ever recorded on earth is about 10 Celsius degrees warmer than that. I've been outdoors at the Jungfraujoch in February, and it was damn cold, but no big deal with the proper clothing.

But for the OP: rent the James Bond movie "On Her Majesty's Secret Service" and the Clint Eastwood movie "The Eiger Sanction" before you go. Both were shot on location in Murren/Schilthorn and Kleine Scheidegg, respectively, and you'll recognize some of the movie locations when you get there.

Piz Gloria, the revolving restaurant I believe was even built for the Bond movie shot at Schilthorn - anyway shot whilst it was being built.

PalenQ - My understanding is that the restaurant part had just been built and the movie company added the helipad and observation deck area as their "payment" for shooting the film there.

I've been there several times - the first was some 13 years ago and it was totally overcast in Muerren. We decided to go up anyway, and maybe 3/4 of the way up the tram broke out of the clouds like an airliner into bright sunshine. The view from Piz Gloria was like looking down on a field of cotton batting with the peaks of the Eiger, Monch, and Jungfrau poking up through it. It remains to this day one of the most beautiful sights I've ever seen anywhere.

The hike Männlichen to Kleine Scheidegg is very different in winter. It goes quite much down first and then up to K.S. Much longer and more exhausting and it will most likely not be groomed that early in December. Forget it.

In December I would forget any hike unless you have snow boots, etc. In mid September a few years back there was ice all around Murren and Grindelwald even at those relatively low altitudes when I was there - it was cold - the passes on the Three Pass postal bus excursion were also blocked by snow that early!