It would definitely go well in your system; you have a nice overclocked Core2Quad, which is an incredible processor by today's standards still. It can keep up with the latest games.
For BF3, your processor should be fine. Right here on Tom's an article proved that the processor does not really matter, unless you have something like a Pentium 4, which you don't. http://www.tomshardware.com/reviews/battlefield-3-graphics-performance,3063-13.html
"Battlefield 3's single-player campaign doesn’t care if you’re using a $130 Core i3 or $315 Core i7. It doesn’t care if you come armed with two Hyper-Threaded cores or four Bulldozer modules...Any reasonably-modern processor is going to be held back by graphics long before hamstringing performance itself."
Skyrim on the other hand is more CPU based and GPU based, but you should be fine. You won't need an upgrade for another year or two maybe.