Can i access my iCloud from any mac computer?

I just got a new iPhone and was wondering
If i could plug it into another computer and access my iCloud from that computer. My macbook's software isn't up to date so it can't run the new iTunes, therefore, my older iTunes can't open my iPhone on it. But i have a mac desktop that has the newest version, though it doesn't have any of my pictures or music. Can i access iCloud from it, thus being able to restore my old phone's stuff and put it on my new one?

"Can i access my iCloud from any mac computer?"
No.
It requires any of these…
-- iOS-based devices running iOS 5 or later.
-- Apple computer running OS X 10.7.2 "Lion" or later
-- PC running Windows Vista service pack 2 or later).

You should be able to access iCloud on your Mac and download the pictures. Just go to the iCloud website and follow the steps in the tutorial. As cloud storage, it should restore your data to your Mac.