In most cases, it's the other way around. Some cool season grasses don't need or like to be cut back short. Others benefit from it. Most warm season grasses require it.

donn is correct. And to elaborate further, any deciduous grass (those that die back or lose color and look like straw or "dead grass" in winter) will benefit from cutting back in late winter or early spring whereas evergreen grasses do not require cutting back and in some cases, resent it.

Thank you both, that clears things up : )

Jen