Next time you're there, try to have a close look at the leaves of the tree - the usual cause of this phenomenon is a heavy aphid infestation, and what's 'raining' down is their honeydew (or their poo, if you like). It's usually sticky once it dries.

There are a lot of willow trees and therefore a lot of 'poo' which is impossible to avoid. Thank you for telling me!

it could also be excess water leaving the leaves as you say they are down by the river.
or a combination of both :o)

Well, at least if it is poo it's not solid! But I prefer the thought that it's excess water as many of the trees have their roots in the water. If that's so, though, why is it always at this time of year and not through the green time?

in spring there is massive growth and leaf extension and the sugars that have been stored in the roots over the winter need to be translocated [moved around] the whole tree. water taken in at the roots are essential for this translocation. once the leaves are fully mature they make their own sugars so depend less on water movement. In the summer the water evaporates faster from the surface of the leaf so you don't get the dripping effect.

What a knowleable lot you are! I'm in awe since I can only identify a few trees let alone know how their systems work.

Thank you for the education. :)