Ha !

Something i can answer !

Ok The statues you linked to are called "Rossbändiger" in German and that translates as "Horse Tamers"

They are not hitting the horse, they are holding the Horses by their reigns.

So the question is still "why ?"

The ones you linked is in front of the parliament.

The parliament was built during the height of historicism in Austria in 1874, and is built in greek revival style. the idea was the greek style would show greece as the source of democracy. Which gives us the first hint that symbolism was a very important theme at the time, in architecture.

So those statues should not be taken literally as a guy taming horses but should be seen as "man taming nature". And in context with the parliament they need to be seen as "man taming Passion" and replacing them with orderly discussion and a fight with arguments and not hate and emotions.

Sources :

Eva-Maria Landwehr: Kunst des Historismus. Böhlau Verlag (UTB), Köln/ Weimar/ Wien 2012

Dehio Wien. I. Bezirk - Innere Stadt, Horn/Wien 2007

Renate Wagner-Rieger (Hg.): Die Wiener Ringstraße. Bild einer Epoche. (Band I - XI). Franz Steiner Verlag, Wiesbaden, 1972–1981

PS : short addendum -

The idea of a man taming a horse having the meaning of "man taming nature" is a lot older - you can also find it In baroque sculpture and if I am not wrong also in antique Roman sculpture.