Your Uni card won´t get you far enough or even near enough to a place, from where you can pedal a DH bike to a decent spot.
I live in Leipzig for decades and never saw a reason to buy a DH bike, even when going by car to the nearest bikeparks (Elstra, Ochsenkopf, Schöneck, MSB-X, Hahnenklee, Klinovec DH). An Allmountain(Enduro) or Superenduro (Freeride) bike will be ok even for the Jumpline in Schöneck or Elstra, plus you can pedal it to a trailhead.
Rochlitzberg has some "Dh tracks", compare it to Trash Mountain, just a bit more elevation. There is a train station in Rochlitz, and in Narsdorf - both about 10km away from the trailhead (see GE).
Best for winter training is
Rosstrappe DH Thale (chairlift), which is open all year round except for now until Christmas. Thale is easily reached by train.
Better to have a car though.
For Allmountain (or Enduro) best places nearby are Kriebstein (from Döbeln or Waldheim), Grimma (Stadtwald), Harz (starting a roundtrip from Wernigerode or so), Zittau and Smrk.
I guess you have checked into
Trailforks already?