Will Safari 7.0 run on OS X 10.6 Snow Leopard? I really like the new Safari in OS X 10.9, but otherwise don't like much else and want to downgrade back to 10.6 -- the last time I was happy using my computer. 

But, can I take the new Safari with me?
No: Snow Leopard runs Safari 5.1.10 at the newest (via and also).

I recommend using Chrome or Firefox if you downgrade back to Snow Leopard. There are messages that Chrome and Firefox no longer support Leopard, but both seem to still support Snow Leopard.