Using colours on headlines or type above about 12 point is ok,
but smaller sizes can be a problem.
What happens is that all printing presses have a small amount of
movement in the positioning of the different colours - the cyan, magenta, yellow and black portions of the print don't line up exactly. Couple this with the fact that CMYK mixes are made up of dots (i.e. apart from the pure CMYK colours most other colours are a mix of coloured dots) means that the finished print can appear to be slightly blurred particularly on fine lines and small fonts.
NOTE: this isn't an issue when using 100% of any of the CMYK colours - it's on smaller percentage mixes that it becomes a problem.
The same thing holds true for white text on a dark or coloured
background. You can do it but don't use point sizes smaller than about 12