1. The president told the people that if they wanted the country to continue to move forward, they should reelect him. He said that to elect his opponent would be like changing horses in midstream.
2. The chairman of the board died suddenly before he could complete his plans for the company. The stockholders were forced to change horses in midstream and elect someone new.

The expression connotes that trying to change horses in the middle of a stream is not a wise thing to do—it would be better to wait until one is on land.