I don't believe you can add new gestures natively in OS X without putting some heavy lines of code in Terminal.
But I think the best solution for your problem is a free app called BetterTouchTool (http://www.boastr.de), which lets you add a large amount of custom gestures. FYI, I just tried out a 4-finger-swipe-down in order to switch to fullscreen mode in Safari and it worked flawlessly.
However, if you want to set up 4-finger-swipe-right/left in order to switch to fullscreen mode, don't forget to disable the corresponding native gesture in the Trackpad System Preferences pane to avoid conflicts.