I al­ways am amazed by peo­ple sug­gest­ing that walk­ing in the rain keeps you dry­er than run­ning. Just saw an an­swer to this. Check it out, it's nice:

I have al­so seen it de­bunked ex­per­i­men­tal­ly, by Myth­Buster­s. But let's try a dif­fer­ent ap­proach: in­tu­itive math. In­tu­itive math is tricky be­cause it usu­al­ly is wrong, but hey, it's fun.

Ap­par­ent­ly, we all agree that how wet you get cor­re­lates to your speed. Oth­er­wise, the ques­tion is point­less be­cause the an­swer is "walk or run, but take an um­brel­la", while true, is cheat­ing, right?

So, for those slow­er-is-­bet­ter pro­po­nents: go and walk very, very, very slow­ly. You may no­tice that you end com­plete­ly soaked be­fore you fin­ish walk­ing. If you did­n't, you are still walk­ing too fast.

On the oth­er hand, if you were to go at 1000000 km/h we all agree you would on­ly get some drops in your frontside, right? Which would not soak you. Right? And most im­por­tant­ly, is con­stant re­gard­less of your speed, be­cause it's just the av­er­age amount of wa­ter con­tained in a man-shaped prism from point A to point B, and you get that wa­ter in your front if you go slow any­way.

As­sum­ing the speed/­soak­i­ness curve is rough­ly monotonous, it's clear that the max­i­mum soak­i­ness is when you go slow­est.

If it's not monotonous, then the ques­tion is rough­ly unan­swer­able, since it would in­volve there is an op­ti­mal speed and it's worse to go ei­ther faster or slow­er than that, which means the an­swer is some­thing like "jog" which is not what you wan­t.

So, go fast, go dry.