Well, I knew next-to-nothing about this, either. (Thank you, American public school system). I came for the fancy sleighs exhibits at the Imperial Carriage Museum, and left a better educated person.
After Napoleon was decisively defeated the European states came together to decide how to divvy up the kingdoms and still retain a balance of powers.  Carriage logistics were a major issue, and the Imperial “Horse Master,” gorgeous personal ride notwithstanding, had to manage it all. And manage it well, he did. Historical records indicate that over 40.000 personal drives were arranged over the 9 months of the Congress.
Think of this as one of the Royal Taxis. After all, a Royal Someone could not duck out for a Schnitzel in their Travel Coach. Quelle horreur! 

As the Congress stretched past autumn and into winter, the Viennese logistics masters were in need of ways to amuse the royalty. On 22 January 1815 a magnificent sleigh ride was organized, with hundreds of mounted guards, footmen, emperors, two kings and other royalty wending through the city to Schloss Schönbrunn for dinner and a performance.

The harnesses and tacks were custom made for the Congress, as well, and many of these pieces, or what remains, are being displayed for the first time.

Of course, no Footman worth his Salz could be seen in the 1815 version of a Jack Wolfskin parka, either. Fine tailored clothing was requisite.

The exhibit was extremely well done and informative, and I daydreamed my way back into the Inner Stadt on my own sleigh, the contemporary U4.