Why will you get rained on more if you’re running as to walking slowly?
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Consider a thought experiment where it’s a steady drizzle that is falling **perfectly straight down**. The rain you collect is based on the surface area of your head (*collecting rain from above*) and the surface area of your front (*as you move forward into the drops falling in mid air*).
**Your front will collect the same amount of rain no matter what your speed is**. If your speed is zero, your front collects no rain, but you make no progress. If your speed in infinite, you collect every drop suspended in the air between you and your destination, Your moving forward is just integrating the average volume of rain between you and your destination.
But the rain that falls straight onto your head varies by how long you spend in the rain. That you can control.
Since you can’t control for the rain you will collide with in front of you (*your speed will not matter*), but you can control how long you are there for the top of your head to have drops fall on to it, **you should go as fast as you can**.
Edit to add tl;dr
tl;dr There is always about the same amount of rain in the volume of space between where you start and your destination. **You will eventually pass through all that space**. You will always collect the same amount of water in the front, no matter what your speed. But you can control the amount of rain on your head. Run.
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