Horses are exposed to full sunburn the whole day over from 10am to 5pm on several places in Vienna, for example
just beside the Stephansdom a few meters in front of the Archbishop Palace
just beside the Burgtheater a few meters in front of the Vienna City Hall
behind the Staatsoper Opera House beside the Hotel Sacher
etc.
none of the actions of several animal protection groups (including Pamela Anderson as PETA ambassador in 2011) brought any change.
(beside the dome, it is the subway which allegedly prevents from planting trees, beside the Burgtheater its the "building arrangement" etc.etc.etc.; but 5m trees can be planted in containers and still provide shadow for the horses, the arrangement of historical buildings can include trees cant they)
Help by building political and communication pressure to those 3 persons, and help finding Austrians abroad who could use their home relations for action
for pictures how it looks pls use "wien fiaker" as Google keywords in Google Images:
farther down the page are pics showing the taxistand-like places where horses & coaches wait for tourists: no shadow is offered there, and temperatures are between 35 and 38 C (95F to 100F) ...