In reply to Sienna78:
Last winter was particularly bad, but normally some ice climbing should be doable at that time of year. Yes, Munich is flat, but ice routes are pretty close by really.
The closest easiest routes are at Sylvenstein, which is 45 mins south of Munich and between Bad Tölz and Achensee. Walk in takes 10 mins from the road to a gorge, where there's about 6x 1 pitch routes from WI2 to WI4. The upper gorge has some harder lines, including a classic 2 pitch WI4. On the same road towards Hinteriß there are other routes, also near Achensee there are routes, too.
In the Garmisch direction you have the Jochburg gullies. Jochburg is before Garmisch, close to Walchensee. These are longer routes and require relatively cold conditions to form. 45 min drive down the autobahn from Munich.
In the Kufstein direction there's a lot, too. Again, about 45 mins from Munich.
Further still, there's Ziller Tal, Sellrain, Stubaital and Salzburger Land. Takes about 2 hours to get to these places.
When you are in Munich go to the shop called Sport Schuster and get the Austrian Ice guide, all these places are in there.