The Winter Running Dance has not (yet) appeared in a book, but think essentially of a set dance from the 17th or 18th centuries where the members of the set all start out about a mile apart. They run to their partners, perform the figures of the set at speed, and run to their next partners (finding them is often a challenge). This is a highly-ornamented version of "run for your lives!" but eventually all the dancers end up at the Unicorn Meadow. Points for speed and grace. And for getting through the whole thing without dropping in your tracks.

The Flower Wars have everything you need for a war--swords, armor, more swords--but it is all made out of flowers. And then everyone fights en meleé and in other set forms. (I have the impression it covers about a week, and obvs in the late Spring when flowers become available.) The point is to get through the entire set of wars with your arms and armor intact.

So it's sort of like the Pasadena Rose Parade crossed with the Pennsic War. With horses.

I hope this answers your question?