My 10th grade rebbe in PIT Rabbi Deren told us the story of when he was on bochur shlichus in FL.
He was walking in the rain with another bochur and they had umbreallas open. An elderly lady stopped them and asked if they were lubavitcher chassidim. After answering in the affirmative she said that she used to take care of the Rebbe's mother. One day there was a heavy rainstorm and she wasn't able to get milk for her. The Rebbe visited and noticing there was no milk he insisted on going out himself to get milk for his mother. The lady handed the Rabbe an umbrella and the Rebbe smiled and asked why he would possibly want to use something that would seperate himself from one of Hashem's greatest blessings.
The lady never used an umbrella since. And the bochurim closed their umbrellas.
I believe it is a pretty known fact that the Rebbe didn't use umbrellas.
I heard a story from Hirshel Lipsker (br"m) that there was a non-Lubavitcher who used to live on Eastern Parkway between Brooklyn and Kingston, who used to sit in front of his house every morning, waiting for the Rebbe to pass by so he could greet him.
One morning it was pouring rain, and the Rebbe walked to 770 just like every morning, without an umbrella. The Yid called out to the Rebbe "ליובאוויטשער רבי, וואו איז אייער שירעם" to which the Rebbe responded "דער אויבערשטער גיסט גשמי ברכה און איך זאל עס אפשטעלן?!"