As far as I found out. It depends on the individual county plus not all cities are the same.. It is rather confusing. I was send a link to
http://www.help.gv.at/74/Seite.740000-16123.html
which gives you info on two austrian cities. One with a muzzle law wherever you go outside of your house(Perchtoldsdorf). The other one Linz where there are certain areas where you have to wear a muzzle. And I also saw Vienna mentioned on another site so I presume I have to call up the city I`m going to be staying at.
Under the english version of the site they have an add on under the keeping of an animal saying
Please note: There are legally prescribed obligations. These regulations can differ depending on the province. A muzzle and leash should, at the very least, always be brought along when the dog is taken for a walk outside.
So I guess it depends on where you are going with your dog.
Why do they make it so complicated and not clear cut????