The fact that one side will quickly win is not (historically) sufficient to prevent wars occurring, even if neither side is certain which side it is that will win.
It could reduce the chances of war, since the most volatile situations are when one or both sides are certain they will win (and have motive to fight, of course). I think these teleporting armies will introduce strategic uncertainty. But I don't think there's any reason to suppose that it must reduce the chances.
This is not necessarily a situation of mutually-assured destruction (although you write in further factors to ensure that it is, if you want the result to be a cold war). It's quite possible that one side will believe itself able to launch a decisive attack, and weather any counter-strike that occurs before it disables the enemies' ability to teleport and/or muster large armies. This is especially the case in the long term, it's much harder to maintain a huge standing army 24/7 ready to teleport than to maintain an ICBM ready to launch as in our own Cold War. I can see a war occurring simply because one side's logistics or economics gives the other side an opportunity for an unanswerable surprise attack.
If nothing else, though, this capacity could make wars shorter simply because there's no limit to the force you can bring to bear (as there is when dealing with fortifications). There's nothing to limit the rate at which those who are going to kill each other, get on with it.
Once someone wins, their main goal will be to keep out of others' hands the ability to teleport an army. Depending on the technology it might not be possible to prevent them teleporting, in which case you'd have to keep them demilitarised at almost all costs. If the victor achieves this then you can certainly argue that imperial repression is "less warfare": there may still be significant casualties but fewer pitched battles. The losing side might not feel that it's any better off under this Pax Imperialis than it was fighting a distant war on its borders, at least not unless any obvious economic benefits kick in, but it's still peace of a sort.
Analogous historical situations? Nothing very close springs to mind unless you do have MAD, because frontier defence has been such an important part of real warfare. The development of aerial bombing by plane and rocket meant that, between 1918 and 1939, the major powers developed a completely new ability to put tonnes and tonnes of high explosive into each others' capitals far behind the frontier. This didn't prevent the Second World War, but I suppose you could think about whether it had a long-term effect separate from the effect of nuclear MAD. I don't know the answer, although I rather suspect that for example the Korean and Vietnam wars would not have happened, certainly not in the form they did happen, if the "locals" had the capacity for conventional (non-nuclear) bombing in London, Paris and Washington.
Going back much further, consider a small, low-tech "warring tribes" situation. Territories are small, fortifications aren't really all that good with the exception of prepared caves, hillforts, and suchlike. A walled border you can't man doesn't do nothing but it doesn't do a whole lot. I'm not sure whether by "almost any point" you mean "except for a few special protected locations", but if so this comparison has relevance, I think. You can't literally teleport anywhere, but if your enemy's territory is only a day's travel across, then you can put such fighting force as you have almost anywhere very quickly. Warfare is neither constant nor particularly rare in such societies historically, and I think prevalence is based on social and economic factors that determine how willing people are to launch an attack more than the fact that everyone is relatively vulnerable all the time.
Another possible comparison is guerilla warfare. It's asymmetric, but it has the property that both sides can move around the territory and in principle attack almost anywhere, there is no frontier. To over-simplify, at any given moment one side doesn't attack because it doesn't know where the other side is, and the other side doesn't attack because it's weaker, has no safe place to muster, and doesn't want excessive losses. Any local change to these factors results in localised combat, so combat is locally intermittent but might well occur somewhere every day.
For another asymmetric example, consider the way that Vikings terrorised England and parts of France for 250 years or so. They didn't teleport of course, but certainly delivered force unpredictably at speed well beyond their "borders". They would simply appear unannounced in a village or abbey, take everything of value, and leave. The English fought back at varying times with varying success, and Wessex had a reasonable try at maintaining a standing army spread throughout its territory to react to raids, but nobody was able to take the fight to the enemy. The Vikings had much of England at some points, lost English territories at others, and many settled and assimilated. It was not a peaceful time.
Ultimately they won all of England, if you count the Normans as Vikings-in-exile ;-)