Ah, the Cliff Walk... A must when visiting Newport in good weather. The views of the ocean are amazing and complimented by the gorgeous homes that line the rocky, walled coast.
Take your time - the "path" can get a little dicey in areas (e.g. you'll find yourself climbing over rocks and wondering if you somehow managed to miss the trail) but keep going - you never know what you're going to see around the next bend.
Definitely wouldn't recommend doing it if the weather doesn't cooperate - I was there in March, but actually had a sunny and somewhat warm day for it. Just dress in layers and take a backpack with a hat and gloves just in case...oh, and don't forget your camera!