How much time do you plan to spend in Europe?

You should be able to find hotel rooms.

Christmas and New years are really family holidays in europe and you shouldn't have trouble finding hotels - many at discount rates - as long as you don;t head for any of the ski resorts (which will obviously have premium prices - since this is the start of their high season). Do expect most things to be closed Christmas Eve and Christmas Day/New Year's Day.

The Christmas Markets open at the beginning of Advent, around the time we celebrate Thanksgiving in the US. They close down about 2pm on Christmas eve. After that is pretty quiet for a couple of days as people enjoy their family celebrations at home. Where exctly are you planning to go and are your dates set in stone. You might have more fun in the week or so running up to Christmas.

Of course you can travel alone - either with a rental car (probably preferable if you are four) or by train or by a combination of both.

Before Christmas it will be very easy to find accomodation, between Christmas and the end of the first week in January, it will be very hard to find available rooms in the ski areas - so better reserve in advance. On the other hand, the business hotels in the cities will be very cheap (Hilton, Sofitel etc.). If it is cold outside, it might be a good idea to stay in a good hotel with a pool and a spa.

For hotel search, you may use www.hrs.com

For cozy, romantic hotels look here:

www.romantikhotels.com

Regarding your itinerary:

If you want to include Germany, Vienna (which is beautiful in Christmas season) AND Switzerland you need a lot of travelling. Either think of flying (e.g. from Vienna to Zürich) or drop Switzerland and see the Alps in Germany and Austria instead (compared to Vienna and Salzburg, the Swiss cities are not that exciting).

In any case, I would include Berlin (a fascinating city, very festive in Christmas season), Dresden, the Romantic Road towns (Rothenburg ob der Tauber, Feuchtwangen, Nördlingen, Dinkelsbühl), Nürnberg, München, the Ludwig Castles, Garmisch-Partenkirchen, Innsbruck, Salzburg and Wien (Vienna). This would make a doable driving itinerary for three weeks. If you include Switzerland you need one week more.

Please check the individual cities for Christmas Market opening and closing dates. Most are closed before the 24th, some may have the last day on the 22nd or 23rd. Some will be open after Christmas.