There is a daily train leaving Amsterdam at 20:31 and arriving in Munich at 7:10 the following day. The trains leaves Munich at 22:47 each evening and arrives in Amsterdam at 8:56. The price very much depends on when you travel, when you book and how much comfort you want to have. Details can be found on the Cityline website.
From Munich you can take a local train to Garmisch-Partenkirchen, at the foot of the Zugspitze. It's a 90 minutes ride. Schedules and prices can be checked at the Bahn's website.
The train continues to Innsbruck. You can consider that as well. In this case, take an accomadation in Innsbruck. There is a small ski resort, the Patscherkofel, accessible from the city center by funicular and cable car. If that's not enough, you have some nice resorts which can easily be reached by a bus shuttle from Innsbruck, such as the Stubaier Gletscher, Schlick 2000 or Axamer Lizum. This way you can spend a nice skiing weekend without having to renounce to the amenities of a city.
The train also calls at Wörgl, from where you have a very quick access to the very nice "Wilder Kaiser" resort.
In case you don't like to take the train, flying from Amsterdam into Munich will probably not ruin you. But it's much less convenient. From Munich airport to Garmisch-Partenkirchen is more than 2h30 and you have the usual airport hassle. And probably less convenient schedules. The night train allows you to get the most out of your scarce time.
If you are francophile, you can consider a flight to Geneva. With Easyjet you will find decent prices. From the Geneva airport you have bus shuttles to plenty of French and Swiss resorts. This will take you 1h30 to 2h00, depending on the destination. Schedules are available on the homepage of Geneva's airport. If "cheapness" is an important criterion, prefer France over Switzerland.
I would also try to contact local tour operators and travel agencies. Chances are high that they have ready made packages just for short ski trips. Eventually, that might be the most convenient option. You just have to go to the office and book it. They take care of the logistics. It is not necessarily more expensive than if you try to brew something by yourself.