I tackle this problem by simplifying. Suppose I am shaped like a rectangular block and the rain is falling straight down. As I move forward rain will either hit the top of my head or my front, nowhere else.
If I go from A to B at the speed of light, there will be no time for rain to hit the top of my head but every raindrop in my path will wet my front.
If I do the same journey slower, my front will still hit the same number of raindrops but there will be time for rain to hit the top of my head. The slower I go the more will hit me. So for a journey from A to B, walking is wetter than running.
If I go for a 30 minute run/walk, however the reverse applies. The rain falling on the top of my head remains the same but the faster I move the farther I travel and the more raindrops will hit my front.
I think the logic remains the same even for a normally-shaped human and windy rainfall.