Rooting will certainly void your warranty. I wouldn't do it if I was in my 30 day trial period.
I also wouldn't suggest doing it if you don't have issues with the software already on the device. My Note is my 4th Android Device. I rooted and loaded custom roms on two of them, and it was simply becuase the software was way to limited. The devices I had were/are a ATT Captivate(Galaxy S), B&N Nook Color, Motorola Xoom and now my Note. Guess which two I rooted: Captivate, and Nook. Stock ICS on the Xoom is great and I haven't found any need to, and all of the reasons I rooted my Captivate are pretty much addressed by the new Samsung software on any GS2 based phone.
The problem is that it is way to easy to screw something up if you aren't sure what you are doing. Fortunately the Samsung Galaxy S phones and the Nook have pretty good tools and are designed nearly brick proof.
Just make sure you have a good copy of ODIN to return to stock if needed. I think it has been updated with a one click for the NOTE. They may even have a one click for the ICS update, not sure.
Rooting for the sake of rooting though can be dangerous. I know i am not going to be doing it unless I start to have major issues with how the phone works.