The iMac model that is currently being sold is the "Mid 2011" model, and according to this support page, your iMac may still be hardware-compatible with Snow Leopard. When first introduced that iMac model shipped with Snow Leopard 10.6.6, then it shipped with Snow Leopard 10.6,7, and is now shipping with Lion 10.7:
It is reasonably likely that the hardware itself has not yet changed, and if so, then I think you may still be able to run Snow Leopard. However you will need an appropriate Snow Leopard install disc. The last Snow Leopard retail disc was OS X 10.6.3, and this will very likely refuse to install when it detects a machine that can only run on SL 10.6.6 or later. Instead, I would call Apple, explain the situation, and see if they will send you a replacement set of the grey-labeled machine-specific Snow Leopard install discs that came with iMacs such as yours before they started shipping with Lion.
If you do mange to get Snow Leopard installed on an external drive in this fashion, you probably would not be able to use its Migration Assistant to transfer stuff to it from the newer Lion volume. I think you'd have to either transfer stuff manually and re-install your apps, or else migrate from a prior Snow Leopard backup.