Should I tip my hair stylist and colorist separately?

Yes. Two separate tips are best. However, remember to take a look at the cost of each service and tip accordingly. If your colorist charges twice what your cutter charges, then their gratuities should NOT be equal.

I've also heard of situations where clients feel 'tipped out' because they've tipped the assistant(s), the cutter, the colorist etc. As a stylist/colorist I make a fair amount of money on my services, therefore, if you feel you need to make a choice about whom to tip, go with the assistant (provided you like their care). You can bet their hourly wage is much less, and they'll greatly appreciate the extra cash.