Well, it could be the snare wires, or it could be your snare heads. Remember that your snare sound is initiated by vibration of the head against the wires, not the other way around.
Your snare heads, like pretty much every other solid object, have a resonant frequency as well as partials or overtones. When something else sounds at those frequencies, it'll cause the heads to resonate, causing buzz. Re-tuning your snare side head to a slightly different tension will change its resonant frequency, possibly to one that's less aligned with the sound from your other other drums, and might reduce snare buzz.
The pitch relationship between the top and bottom heads on your snare can be a contributing factor, too. If they're tuned to the same pitch, you'll have a very resonant drum. If they're tuned to a consonant interval (like a major third, for example), you'll still have a pretty resonant drum, which can promote bottom head vibration, and in turn, snare buzz. Re-tuning your bottom or top snare head will alter the pitch relationship between the heads and can alter the amount of buzz you experience.
Have you checked to make sure your bottom head's in balance? Tap about 2" in from each of the lugs and make sure the pitch at each lug is even. An out-of-tune head might be a source of extra snare buzz.
Have you checked your snare wires to make sure that you don't have any strands that are bent or under less tension than the rest? Stray snare wires can cause some major headaches. The fix in this case is to replace your snare wires.
If you replace your wires, consider picking up a set with fewer wires if you want to reduce buzz. I've got one drum that buzzed like crazy with 20-strand wires on it. Replacing those with a 16-strand set completely fixed my problem with sympathetic buzz and the drum still sounds fantastic. In fact, I like the 16's better. I hear a little less snap from the snare wires, but more tone from the shell.