One of the most famous ski mountaineering trips in Austria is the so call "Rumpler-Runde" around Dachstein, optionally including Dachstein summit as well. The ascent onto the plateau of Dachstein mountain is very relaxed, as the majority just ascents with the cable car, for the way down there is a skiing slope, which offers also very late in the season still reasonable snow conditions. It can be done as a day trip, but more relaxed and rewarding will be, if you include a night. Like this we have been at the peak just in late afternoon without any other people and just skied down in dawn to our hut. My trip took place in April 2022, at Easter.
Taking a train from Vienna/Linz to Obertraun. Some are even direct connections, all the way from Vienna. At Obertraun Bahnhof you can decide if you walk the 3 km to the cable car or take the bus, like in the screenshot shown below.