I believe the answer depends on whether you more closely approximate a flat plate or a sphere.
If you're a flat plate (surface perpendicular to the direction of travel), then the increase in your raindrop cross-section as your velocity increases exactly compensates for your reduced path-length through the raindrop rest frame, and so your velocity makes no difference.
If you are a sphere, then you get no change in raindrop cross-section with your velocity, so it pays to reduce your path-length in the raindrop rest frame: you therefore get less wet if you move quickly.
So rotund people should hurry; slim people may do what they wish.

Grant Hutchison