What I prefer over downhill skiing is cross-country skiing. And the mountains south of Zittau are just perfect for that! A first look at the topography might make you sceptic, but believe me, there are many well groomed cross-country tracks all over this area, connecting the villages with each other, leading from mountain hut to restaurant to hotel.
There is a track mostly along the German/Czech border called "Kammweg" (means path on the crest). Elevation is always above 500 m (which makes it quite snow reliable). This track leads from the western to the eastern end of the Zittauer Gebirge - experts can do it in one day, beginners and intermediates split it in two parts and stay overnight in Jonsdorf e.g.
But there are easy and shorter tracks around all the other villages as well. No shortage of groomed cross-country tracks!
Equipment: Bring your own or rent in one of the sports shops/rental stations - Zittau, Waltersdorf, Jonsdorf or Oybin.
Although the altitude is rather poor - the mountains south of Zittau are quite snow reliable due to their eastern location.
The elevation difference is of course little - 200 m are maximum. Do not expect skiing opportunities as in the Alps or Rockies! But locals (and even Berliners :-)) do enjoy the runs in Waltersdorf, Lückendorf, Oybin.
The best skiing ops offers the small area in Waltersdorf. There are a couple of skilifts at the foot of the Mt. Lausche (793 m) incl. snow cannons and halfpipe for snowboarders. Runs are always well groomed with modern machines. Parking in Waltersdorf, free shuttle bus to the skilifts. Night skiing possible.
Equipment: Bring your own or rent in sports shops/rental stations in Zittau, Waltersdorf, Oybin
For those who do not want to do extreme sports, but spend some time in a beautiful landscape with outdoor activity is rowing a good alternative.
There is a small lake, rather a pond, in Jonsdorf in the Zittauer Gebirge where you can rent a boat for little money. It is fun rowing for a half hour and then sitting in the neighbouring beergarden and watching the others :-)
Even the kids enjoy the rowing.
Equipment: Rent a rowing boat in the restaurant "Zum Gondelteich" (actually in their beergarden).
The bizarre sandstone rock formations in the Zittauer Gebirge are perfect for climbing. Although not as large and famous as those in the region south of Dresden (Saxon Switzerland) they attract a lot of locals who like outdoor activities.
On the picture you can see a well maintained "Klettersteig" (climbing route with fixed iron hooks etc.) near Jonsdorf at a rock formation called "Nonnenfelsen". It is very popular especially among intermediate climbers. It is 350 m long and takes about 30 minutes.
Equipment: Bring your own or rent in sports shops in Zittau, Jonsdorf or Oybin.
For more information ask the DAV section Zittauer Bergsteigergemeinschaft.
The Zittauer Gebirge (mountains) south of the town, right on the Czech border, is excellent for hiking/walking. It offers more than 100 km of well marked and maintained hiking/walking paths, from short walks to day hikes.
The elevation of the villages in the valleys is about 400 m, the mountain tops reach almost 800 m (Lausche 793 m). The paths to the tops are sometimes quite steep due to the topography of the mountains - former vulcanos! There are also bizarre sandstone rock formations to find - but this is another tip (climbing).
However, do yourself a favour and hike to one of the mountain tops - the views are fantastic. You can see far into the Czech Republic to Mt. Jested above Liberec (1020 m) and the Jizera Mountains (1122 m), with good luck you can even see the Krkonose (1602 m).
Equipment: Nothing special needed. Bring good shoes, preferably hiking boots, but jogging/sports shoes are sufficient.