Cecil Moore wrote:

"Atmospheric Electrostatics" is a 120 page free book
available for downloading at:

http://www.colutron.com/products/cosmos.html

Here's a quote:
"In contrast to rain, precipitation currents carried to
ground by snow are usually always negative under
potential gradients between +/- 800 V/m (Chalmers 1956).
The total precipitation current around the earth is
estimated to be about +340 amperes."


So that would give a current of about 0.06 picoamperes per square foot?