If I'm playing as an eastern faction, I always prepare to defeat the horde almost as soon as they arrive (although I've never enjoyed fighting them in Khazar). Playing as a western faction, however, I prefer to leave them well alone and let them weaken my neighbours by attacking them from the east.

By the time the horde have filled the steppes, their forces are so scattered that they're rarely a threat any longer, meaning that when the time comes you can pick off their provinces relatively easily.