Is it haram for me to go to the color run, which is mixed, given that I will be accompanied by my friends (all girls) and an adult who will be there to supervise?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger. 

The Muslim woman is allowed to play the sports that suit her nature, be it running or otherwise. However, the relevant sharee'ah provisions and Islamic manners, such as practicing sports without mixing with non-mahram (marriageable) men and without being seen by them, should be observed. It is possible that the woman's body may be exposed or outlined while practicing the kind of sports that you mentioned.

Hence, it is impermissible for you to join this run given this environment that violates the sharee'ah, even if in the company of a female supervisor or female friends. Their presence does not change the relevant religious ruling.

Allaah knows best.