Depends. If it's a Late 2011 model, then it cannot be booted by a Snow Leopard system. If it's prior to Late 2011, then it can be booted from Snow Leopard 10.6.8 or from the original installer DVD that came with it new. You would need to put the old disk into an external enclosure in order to clone it to the newer disk or be able to connect the two using a Firewire cable. Cloning would then be done using Target Disk Mode.
Otherwise, don't clone anything. Install the original OS onto the newer disk in the newer computer. Then simply transfer the user account with the Migration Assistant.
How to use Migration Assistant to transfer files from another Mac
Migration Assistant tips and tricks