Very feasible. I went up Zugspitze yesterday. Get a bus or train to Garmisch and from Garmisch take the Zugspitzbahn. Public transport is the best option. A car is a liability.Edited: 02 August 2015, 19:53
You may like to do the round trip. From Garmisch take the Zugspitzebahn as mentioned in #1, then the short cable car ride to the summit. For the return you can take a cable car to Eibsee and walk around the lake, then catch the little train back to Garmisch.
I normally recommend the route & itinerary that EmeraldDiva notes -- but I usually recommend taking the Eibsee bus back to Garmisch, then getting off at the Marienplatz exit and walking through town to go back to the train station.
You can use the German rail site to get all the schedules --
Departure: Füssen (or Fuessen)
Arrival: Zugspitze Bf Zugspitzeplatt
It shows that if you leave Füssen at 08.03, you can arrive at the Zugspitzplatt (the glacier, not the summit) at 11.28 with 2 changes (in Reutte and Garmisch).
Have fun as you plan!
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