How do I use dynamic paint to control hair density? I tried using the dynamic paint modifier to control the hair density of an object but it didn't work out like I wanted it to.

First is set up a plane, gave it a few subdivisions and added a dynamic paint canvas. The canvas is set to weight paint mode and I assigned a vertex group to write the data to.
Then, to paint the canvas I added a sphere as a dynamic paint brush and placed it inside of the plane. The sphere has a basic animated path through the plane.

I'm just using a simple hair setup with basically no settings changed.
The only changes are in the vertex groups panel. There I, obviously, tried assigning the vertex group from the dynamic paint to the density slot, to no avail. The exact same vertex group can be used in the length slot and the effect will be seen.
When I use normal weight paint with the vertex group i can control the density.
I also tried swapping the two modifiers in the modifier stack and enabled the use modifier stack option in the particle settings.

Any ideas how I can solve this problem?
Pre-bake the dynamic paint. Generate a group on the final frame. 
Pre-paking simulations is the key to what you´re looking for. Blender manual mentions this but doesn´t cite any practical examples.