Okay, we can look at our path through the rain as a volume... assuming an even distribution and a constant rate of rainfall, then each cross-section of that volume will have the same amount of rain at each moment in time. So, your speed through that volume doesn't matter if you are out in the rain for the same amount of time for both walking and running, but in reality, the point of the running is to get under shelter, so you will spend less time under the rain, thus getting less rain on you. Running or walking makes no predictable change to the number of rain drops in your path at any given moment.