This is now exactly how it works to take a screenshot on Samsung Galaxy Note that already upgraded and running with Android Ice Cream Sandwich ICS 4.0.3 OS. Once you already updated your Galaxy Note to ICS, the screen capture hotkey combination is now change to Volume Down and Power buttons (originally [Home] + [power] when it was in 2.3.6). This function was the same on Samsung Galaxy S2 that also updated with ICS 4 OS and probably will work on other Samsung android devices that already runs with said Ice Cream Sandwich OS.
You'll just then simply press and hold the Volume Down and Power buttons at the same time for about a second. You’ll see a flash and the screen will be framed which shows the screenshot was taken. A new notification in the notification bar saying "Saving Screenshot" and once it’s done there’ll be a "Screenshot captured"” notification in the pull down menu which will take you directly the screenshot in the Gallery.
The screenshot will be saved on your phones internal SD card - in a folder /Pictures/Screenshots. That's it, enjoy!