Lot of "Zimmer Frei" notes do not really mean it
It is true that there are lot of zimmers (rooms for rent) along the tourist roads like "Alpenstrasse".
Indeed you see many of notes as you pass by. But this does not mean you easliy get a bed for the night.
We left one last night for chance and it took several hours to find a place.
It was Monday and we needed a room for one night. Several places that had the standard "Zimmer Frei" (room available) sign posted were closed for their own vacation or other reason.
One lady first agreed to rent, but then refused - one night was not worth it. for her.
At the end, after driving some 15 extra km , following signs to Zimmers, we did find a place to stay. It had more beds than we needed, and was much more expensive than we planned to spend.
Bottom line - it's worth spending extra time on preparation and booking a room in advance. you'll save time on the road, money and some frustration.