Backup for downgrade from Mavericks to Snow Leopard on smaller Hard Drive?
It can be done but involves a lot of juggling.

Your best option would be to shrink your existing partition, create a new partition then install Mavericks into the new partition.
You need to boot into recovery mode (or from the Snow Leopard CD) to shrink the partition (using Disk Utility) as you cannot resize the active partition. You can copy existing data from the original partition during installation.