I don't think so. Zangetsu hates rain because Ichigo hates rain, since it was raining when his mother was killed.
I thought it was more symbolic than that: Zangetsu hates the rain because when Ichigo is upset it rains in his inner world, and Zangetsu doesn't like it when Ichigo is upset.
He fears his fate too much, and his reward is small, who will not put it to the touch, to win or lose it all.
-James Graham, 1st Marquess of Montrose
Satomi by Elagune