Disclaimer: Like many other, I abhor and reject all terms including "cyber" except "cyberspace" in its proper meaning (see William Gibson's novel "Neuromancer") which has very little in common with the Internet or any other present-day technology.
That said, yes - "cyberwar" is entirely possible and would be immensely harmful. But no, we have not seen anything even slightly related to full-blown "cyberwar". If it happened, we would notice: trust me. It would blow the doors off computer systems most people have no idea exist: systems that give them power, light, water, network access (of course), banking, medical services, education, food, etc. etc. Our present posture in this respect is basically that of a person camping in the woods who has been told there are grizzly bears around, and whose response has been to tie himself up stark naked and hang himself from a tree at convenient nibbling height.
It must have been about 20 years ago that I began lecturing and writing about the security risks of software systems. I always kept it as short and simple as I could, since I realize that security is not only very counter-intuitive but (to most people) appallingly boring. But I usually wound up with a warning: there were many threats, ranging from the trivial to the extremely serious; there was hardly any defence; and hardly anyone was taking the trouble or investing the resources to put up any defence at all. The only good news, I added, was that so far criminals had made no real efforts to exploit all the juicy vulnerabilities spread out before them. That wouldn't necessarily last, I warned.
The same remarks, mutatis mutandis, apply to "cyberwar". It would cause far more harm than criminal exploitation, because the objective of war is to bring about complete defenselessness and unconditional surrender. Look at Iraq after the second Gulf war, and imagine that happening to all the IT infrastructure you know about (and that you don't know about). And, due to the design of the Internet and the amazingly insouciant carelessness of governments and corporations, our infrastructure is almost completely unprotected. What we have seen so far is analogous to a few spies and skirmishers probing the most obvious weaknesses. They have deliberately refrained from even hinting at what they could really do, because (as Sun Tzu pointed out)
"Speed is the essence of war. Take advantage of the enemy's unpreparedness; travel by unexpected routes and strike him where he has taken no precautions".