The color dust used in the run is very fine, tiny specs, made to stick on people as they run by. This kind of dust penetrates even the pro-level lenses and pro-level cameras with all their supposedly weather sealing. Because the dust is made to stick it doesn't blow out like regular dust, it needs to be wiped off.
1. Seal off your camera gear
This is where a plastic "rain cover" bag like OP/Tech Rainsleeve comes in handy. It has two major openings, one in at the front of the lens and the other "under" the camera - designed for sliding your hands into the cover for better access to control the camera. I would seal that off completely. For the viewfinder there's a small hole in the rain cover to slide it over the viewfinder. When that's properly sealed off you slide the rubbery eye cup over it.
Best lenses for these kind of situations are those who do not extend. Those are much more likely to pick up some dust and get it into the lens. Either use a prime lens (without zoom) or use a lens that does not extend like the lens I used, the Canon 70-200 2.8L/IS. The 70-200 doesn't change its size while using the zoom, all that action goes on inside the lens body. Also, do NOT change lenses. If you need two lenses, you're going to need two camera bodies.
This is a situation where you definitely should be using a protective filter. Replacing that is cheap and could save you a lot of trouble.
2. Don't open up the camera cover unless you really need to.
Have your largest memory card in the camera so you won't have to change memory cards as often or even at all.
You might even consider shooting lower resolution raw files in order to fit more photos onto the card you're using. Do you really need +21Megapixel photos or would +10M do ?
Make sure your battery is fully charged and in good working order. Might even use a battery grip for longer use.
3. Lens cloth
You are going to need to wipe the front of the lens numerous times so keep yourself stocked up with a few lens cloths.
4. Don't forget to have fun!
This a fun event so don't remember to have fun! Just have your gear as protected as you can - then you're all set for a fun time at Color Run.
5. Vacuum clean do NOT blow!
After the event your gear is most likely all covered in color dust. Vacuum it clean, do not blow.
Here's how I protected my Canon 5D Mark II for Color Run photoshoot.