I've never found any decent English language books for that area, but there are some excellent German ones which you could pick up once you're there. And check out
this site.
The obvious thing to do in the Garmisch area is the snowdonized Zugspitze with its railway and restaurant. There are plenty of quiet walking routes to the top.
It's also a great cycling area, with plenty of books available. Garmisch is really only on the edge of the Alps, and if you go a little further south or east there is lots more to do.
If you have only three free days available, I'd think about devoting some time to non-walking activities. Berchtesgarden, Dachau, the Kehlstein, Salzburg, the Fernpass (cycling or driving) and Munich itself are all worth a visit.
Oh, and ice gear and insect repellant are not necessary