Most launchers do not require root to install. Nova, GoLoauncher, Launcher Pro etc you just install them and the next time you hit the home button it will ask you which one you wan't to use-default Android or the newly installed. You can choose for it to remember this decision and just use that one from now on.
Now there are SOME features of launchers that you may not be able to use unless you root your phone. Some people prefer to have a "stock" Android experience. This is similar to what you'd have on the original Droid, Samsung Galaxy Nexus and now the Nexus 4. It's Android without any customizations and skins. Basically if you took Motorola's MotoBlur, HTC's Sense UI, Samsung's Touchwiz out of the equation and left the phone a standard Ice Cream Sandwich or Jellybean phone.
When you are rooted you can flash a ROM that is either it's own crazy skin, (Cynaogen etc) or is AOSP (Android Open Source Program) which is basically a stock ROM for THAT particular phone. Consider AOSP = vanilla.
A "stock" ROM for the Note 2 would be something that has Touchwiz components enabled and working, but removes all other bloat. Now these ROMs can have their own launchers built in and usually have many features Android OS is just catching up to.