You don't colour the fur, you have to attach the fur to a material so you put a colour map on the material and have the fur take it's colour from the underlying material.
I'm sorry but I can't recall the settings off the top of my head and I don't have time to open Maya right now but maybe someone else can post the settings you need to set in the attribute editor.

Ok I had a quick look and in the fur description tab you can map a file to the base color and tip color, so if you have a colour map you have painted in say Photoshop you could map it to both the base and tip to get your coloured fur.You can bake the colour to the fur there also.