I've talked about this a few years ago, so this'll probably be a rehash of that older post (if someone else can track it down for me).

But in essence, the problem is that the way we conceive of wizards and magicians in warfare is based off of Dungeons and Dragons, which in a certain way, reskinned WW2 wargaming classes onto fantasy medieval combat. Fighter = Soldier, Cleric = Medic, Thief = Scout, Mage = Artillery.

So your conception of a magical battle is basically a reskin of WW2 backprojected onto fantasies of premodern battles, which have no real bearing on how those battles were fought.

The other problem, is "magic" is very hard to define, because of the problem of "magic" being an accusatory pejorative, thus making it difficult to differentiate it from say, religion or science. i.e. "your magic is my religion" or "my science is your magic."

We want magic to be illicit and otherworldly, it's what gives it its spice. If magic weren't illicit, it would be accepted, it would be something as bland as... well... religion or science.

So in that regard, what's the difference between "wizards hurling fireballs" vs. "holy men summoning angelic armies (2 Kings 6:8-23)" vs. "finding an enemy army by tracking the flights of birds over a forest"?

Because priests (religion) and engineers (science) frequently accompanied premodern armies into battle. Are they magicians? Is a successful prayer for rain, destroying an enemy's fire attack a spell? Is a lit trebuchet projectile a fireball?

As /u/bitparity pointed out, "magic" is hard to define and is often used exonymically (that is, a group says of another group that what that other group is practicing is "magic"); this can take two forms: either it's used for something not understood, but evidently possible, or, on the contrary, it is used for something which is per definitionem impossible. This is how Frazer defines magic in The Golden Bough, an extremly influential work of early anthropology: it's the "false science". It's theories about how to influence the world which are based on a mistaken understanding of the laws of nature. He contrasts this to religion, because religion is essentially a social affair: I'm talking to an intermediary and ask him or her or it to change the world for me. Magic does away with the intermediary and gives me the means to influence the world myself - it is, Frazer says, therefore far more closely related to science than it is to religion - something that might strike a modern audience as odd. So, that's two etic (that is, externally-assigned) usages of "magic" already.

The issue is further compounded because terms from other times and cultures are not always readily translatable to "magic", and we seem to largely apply the term according to I know it when I see it. And that is, I think, where /u/bitparity might have gone wrong: it's true that it is therefore meaningless to ask whether there ever have been incidences in which one group used, for military purposes, anything that another group designated with a term which we may or may not translate as "magic" (e.g. the "thunderstick" of the white man), but we can meaningfully ask whether there ever have been incidences in which there have been applications of something that fulfill anyone, or a specific, of the numerous definitions of "magic" that are current in anthropology, the issue not appearing to be that "magic" is impossible to be defined, but rather that it is impossible to be defined to the agreement of the field.

Here's two possible ways in which we might be able to answer the question more accurately:

Besides providing us with the "false science" definition, Frazer also provided us with two laws that magic supposedly presupposes, although whether they are part of the definition, or a synthetical predication, is unclear: it functions according to the Law of Similarity and the Law of Contagion, collectively known as the Law of Sympathy. What they are isn't really important at this point, but I would like to propose that finding a nomological basis might lead to a meaningful way of asking the question: for example, to a modern audience, it might be sensible to ask whether there were established practices that attempted to do things that violated the currently-recognized laws of nature.

Alternatively, simply going by "false science", even when going beyond the strict nomology provided by Frazer, might not be the ideal definition: all sorts of things, such as miasma theory, or the geocentric model of the solar system, would fall under this definition. In A General Theory of Magic, Marcel Mauss detailed that we do not seem to be thinking of magic simply in terms of rules, but in terms of a certain constellation of practices, practicioners and institutions: it is specific practices and specific "false scientists" which make up magic. Probably, you wouldn't limit yourself to supposing that they attempted "throw fireballs" or "summon dragons", but we could ask whether there were any instances of things that - I know it when I see it - appear to be "magic" to our contemporary audience.

You might be interested in a past post on the role of "Owl Men" in Mesoamerican warfare, particularly the comments from /u/islacoatl and /u/quedfoot.