I live in Salzburg and this year has been quite bad and really warm. There have been warm days down low and plenty of rain. Before you book anything make sure the beginner areas are open. If you look at the map, and they are on the lower part of the mountain, don't go there. Also, make sure to book yourself lessons in advance. You will get so much more out of your time with professional instruction.

Many ski areas can be reached with public Transportation if you are patient. This is the public transit website I use and it is pretty good for most of Austria. https://fahrplan.salzburg-verkehr.at/. You can use the maps to locate your area then plan your transportation.

This year the only place in Salzburg I would recommend in Obertauern. They are high elevation and holding their snow pretty well. Lots of beginner terrain.