To dream that you are participating in a race is an indication that the people around you are jealous of the goals that you have accomplished. They will conspire to obtain those things for themselves. Winning the race signifies they will not be successful in their endeavor.
Conversely, this dream may be a reminder that you need to stop and smell the roses or to find another path for your life. Finally, in many cases, the race dream is a symbolic representation of your inner competitive nature.