I absolutely love my army of cavalry but at the end of the day it has to be accepted that Archers do the trick better in most situations.
A wee piddly rainbow and you toss them outta the way, cav get slaughtered.
makin' a heavy timin' and clearin' the rainbow before the cavalry comes runnin' in works..but personally I wouldn't want my main archer army relyin' on the lives of a few wee pikes and swords...damn get pure thousands of them! Make sure they don't jus' have to warrior bomb you a few times to clear your rainbow.

Or hell, do what I do and jus' have some cav in the way of the archers. Heavy rainbows, cav, archers and ATs...fun stuff to attack...