I found out recently, after trying to boot my El Capitan Macbook Pro from a Snow Leopard ext hdd that Snow Leopard cannot read anything from the El Capitan drive. The other way round is ok though.
The best thing I can think of would be to reinstall the Time Machine back up to El Capitan, then do a manual drag and drop back up of your data to another drive before installing Snow Leopard then dragging and dropping your backed up files to your fresh Snow Leopard install.
This is because (if i remember correctly), time machine back ups are hard to browse. I always use Carbon Copy Cloner as it makes a bootable copy of my drive and you can also easily access your files if you plug it in as an ext hdd.
You only really need to back up your home folder and just make sure your Keychain and browser folders are backed up, then reinstall all your apps. Maybe a bit more difficult if you have a lot of paid for apps.
This is what I would do, but maybe someone else has a much better idea.