Central Europe in December?

2 week trip for Germany, Austria, Czech Republic, Switzerland
Fly into ...
Berlin 3 nts
Dresden 1 nts
Prague 2 or 3 nts
Vienna 2 or 3 nts
Salzburg 1 or 2 nts
Munich 2 nts
Luzern 1 or 2 nts
Fly out of Zurich

Towns will not be shut down, the Christmas markets will be in full swing. If you want the ultra-Christmas experience . . . see my post on another December travel question. The markets filled about every square in the historical town centers. If you want details, PM me. I visited about 11 different cities in 11 days.

Larger cities are not going to "shut down for the off-season". Museums and historical attractions will stay open all year round, and shops will be very busy as the Christmas shopping season ramps up.

If you have 2 weeks, I would stick to only three or at most four destinations, to avoid spending all your time travelling. There are some very scenic rail and road routes in that area, but not all of them are.

I don't know what the weather is like in the Rockies, but I would be less worried about very cold weather than the kind of constant overcast and drizzly rain that may happen in December, and can be quite depressing. It's more likely than picturesque snow at that time of year.

If you intend to travel between your chosen cities by train, you can get significant discounts on the fare if you book 90 days or so in advance. Buy tickets from the national rail companies - for international journeys try both the starting and ending country and see if one is cheaper. It'll be the same seat anyway, it just varies how much discount you get. This will usually be cheaper than a rail pass if you're just doing a few city-to-city trips.

Germany: www.bahn.com
Austria: http://www.oebb.at/en/index.jsp
Switzerland: http://www.sbb.ch/en/home.html
Czech Republic: https://www.cd.cz/eshop/default.aspx

Phillip hit the nail over the head. Towns, for the most part, don't "shut down". Most monuments or cultural attractions remain open all year, although many with reduced visitation hours.

The weather in those locations can get cold in Decemeber, but temperatures are more likely to hover well above freezing (the Alps being an exception). As noted above, the atmosphere is usually damp and gray, and what sun you experience is usually low in the sky. So, the scenery in the countryside is much more low yield, but these conditions affect your enjoyment of cities far less.

If you have to go in December, it's better than not at all. The weather is described above, most likely gray and cold but not likely below freezing temperatures. It may seem surprisingly cold, possibly colder than freezing weather at home, because of the dampness. The worst part, from my perspective, is the short daylight hours. The best part are the Christmasmarkets and general lack of crowds. Sights, such as museums, are open year round, as are hotels and restaurants.

Family in Munich, then Vienna, Prague and then?

Saxony is Germanys Christmas country and just 2 hours away from Prague. Most German Christmas traditions come from this region (+ Thuringia):
Longing for light
Germany's Christmas toy towns
The German towns that Christmas traditions sprung from

You could use Dresden, with one of the biggest and oldest Christmas markets, as a base for day trips to nearby towns (Ore mountains), or see it in combination with Erfurt, which offers the only big German Christmas market (200+ stalls) in a completely preserved town.

2014 was the 4th trip we took to Germany, during December, since 2009. I checked my notes and I have only had to use my umbrella twice. All 4 trips were completed by December 21st. I live in Dallas but grew up in Michigan so I know cold...I have been uncomfortably cold only once - in Nuremberg on the 2009 trip as it was very windy that day. And even that day the temperature, during the day, was above freezing. While the markets are crowded (especially week-ends) other sites are usually line-free. We only travel now during the shoulder season and early winter to avoid crowds and avoid the heat. Yes, darkness comes early but the markets are more enjoyable when all the lights are ablaze and locals congregate for gluhwein ..... A wonderful way to wrap up a day of, relatively crowd free, sightseeing. Schedule your outdoor sites between 10-3 - save indoor sites for after 3. Layer well and you will love it!

Yes, darkness comes early but the markets are more enjoyable when all the lights are ablaze and locals congregate for gluhwein

Exactly. Some of my best memories from my time living in Germany were just such these occassions, particularly when I knew people there.

Hamburg:

Average Temp 35
Average High 39
Average Low 31
Average Rain days 12 (40% of the days)

Frankfurt:
Average Temp 36
Average High 39
Average Low 30

Munich
Average Temp 33
Average High 37
Average Low 28
Average Rain days 15 (50% of the days)

Berlin
Average Temp 34
Average High 37
Average Low 30
Average Rain days 16 (51% of the days)

Budapest
Average Temp 34
Average High 37
Average Low 30
Average Rain days 12 (40% of the days)

Arrivals in Munich for instance. Looks like the only appreciable drop in tourism is in Jan, Feb, Mar, April and Nov. Even then its only a drop of 20% to 30%. And this year the "shoulder months" are approaching the same figures as last years high months.

2014 Actual
Jan 420,000 (2015 = 439,000
Feb 418,000 (2015 = 452,000)
March 491,000 (2015 = 529,000)
April 512,000 (2105 = 530,000)
May 582,000
June 550,000
July 646,000
Aug 630,000
Sep 622,000
Oct 637,000
Nov 514,000
Dec 554,000

Don't you just love the Germans. They keep count of everything in such detail.