If you use Safari, that is tied to the operating system an cannot be updated.
This way alll you have to do is download, install and use an alternative web browser, instead of upgrading your entire Mac OS. Snow Leopard OS X.6.8 is a very old operating system. The 10.6.8 update is recommended for all users running Mac OS X Snow Leopard and includes general operating system fixes that enhance the stability, compatibility, and security of your Mac, including fixes that: Enhance the Mac App Store to get your Mac ready to upgrade to Mac OS X Lion. The ESR version 45 of Mozilla Firefox is still completely secure.
Mozilla will issues ESR (security) updates to OS X10.6-10.8 for the version 45 of Firefox, but will not get ANY new web browser functionality feature updates. Mozilla will keep issuing security updates for Firefox in the form of their Firefox ESR web browser (Extended Security Release web browser program, vers. Mac Pro, Mac OS X (10.6. If you need a more secure and compatible web browser that'll use the current Adobe Flash Player, switch to using Mozilla Firefox's web browser version for OS X 10.6.8- 10.8.5 here. If you are still using the version of Safari for OS X 10.6.8 Snow Leopard, that Safari version is very old, hopelessly out of date and no longer secure and you should stop using it ASAP, if not sooner! Slimmer QuickTime Player: QuickTime X features a simplified GUI with a greater focus on codec support. This version of Apples OS also has a reduced footprint. This update does not have stacks of new features, rather overall improvements and efficiency upgrades. Here's a much easier option for you until next Spring. If you updated Safari to version 5.1 and then applied the OS X 10.6.8 v1.1 update, you will need to redownload the latest version of Safari again. Mac OS X 10.6.8 Snow Leopard is an upgrade to the previous version of OS X Leopard.