In general, you can ride a mountain bike on all public roads in Austria. Of course, there are exceptions such as motorways, expressways or pedestrian zones that are commonly closed to bicycle traffic.
Biking and cycling on forest roads or alpine paths is regulated differently from federal province to province. In most of provinces biking on such trails is currently forbidden by law. Not so in Tirol, where the "Tirolean Mountain Bike Model" has been introduced already in 1997. It guarantees all bikers that they are legally biking on the marked paths and trails ("BERGWELT TIROL MITEINANDER ERLEBEN" logo). In Ötztal, Tirol's longest side valley, biking and cycling fans will find an approved mountain bike route network of over 850 kilometers. HERE you will find all MTB routes in Ötztal.