Some highways in Austria close for the winter season. For example, the Grossglockner High Alpine Road is closed until sometime in May.
Where can I find a map that shows which roads are currently open/closed?
The information you're looking for is which mountain passes are open/closed. Here's a site (in German) detailing the situation in Austria, as well as Germany, France, Italy, Switzerland and Slovenia. Purple/red means that the passes are closed.