The invention relates to a device for preparing milk froth that can be optionally hot or cold, or for dispensing optionally hot or cold milk (1), said device comprising a milk container (4) that can be removed from the device, a milk inlet which connects the milk container (4) to a cold froth device via a milk valve section, said cold froth device being activatable by means of an air valve section, and comprising an outlet line (15) that is located downstream of the cold froth device and comprises an outlet (16). The milk container (4) can be inserted into the device (1) in a guided manner and the base (4a) of said container is equipped with a milk snap-in valve (17). A complementary receiving section (17a) for the milk snap-in valve is fixed in the device (1) and is formed as a milk inlet directly on the milk valve section. When the milk container (4) is inserted, the milk snap-in valve (17) engages in the complementary receiving section (17a) for the snap-in valve and is locked therein.