Imagine Mice are the sentient species on earth. Predators like snakes, owls, hawks are still a threat. Would wars between factions still involve large groups of mice travelling together and pitch battles or do you think moving around like this would be too dangerous?
Apex Predators Do Not Take On Herds
And an army is a very well trained, resilient herd with many spears. Every predator is looking to get the easiest meal they can, so they are looking for stragglers or to isolate individuals. This is actually similar to armies, which also want to isolate smaller sections of their enemies and pick off stragglers. Instead of eating, though, armies are looking to control territory.
But Military Operations!
These will hardly change, there is just another threat to worry about. Good commanders secure and protect supply lines, even against apex predators. Smaller forces (or Hannibal) can raid and pillage to sustain themselves.
An Exception: Kaiju
In which case, everyone dies anyways and war is not part of your story!
If the predator is large enough that no combination or number of medieval weapons or poisons can harm them, mankind has bigger problems than fighting each other. It's an apocalypse and no one is waging formal war. Maybe raids and small groups/tribes, but not massive and organized war. War in the time of Kaiju, though intriguing, usually isn't the point of Kaiju stories.
Edit: From comments, I suppose I should clarify this section. I use Kaiju for their "unstoppable, uncontrollable force" aspect. Kaiju represent the most extreme case of a predator. If a predator has such qualities, we are looking at a breakdown of society in proportion to the predator's appetite. The question is very details light, but I feel like I had to account for such a situation but also point out that wartime logistics and strategy is unusual for the Kaiju genre. Arguably, these stories are about big monster battles ("spectacle"), distruction, forces beyond mortal control, and/or forces which shouldn't be in mortal control. (Original Godzilla, in context of Japanese culture at the time, sure does look like a stand in for nuclear weapons.)
Presumably marching around in huge columns would be a big target for predators
This presumption is incorrect for the vast majority of predators, especially those that have some co-evolution time with humans. Primarily because it is very high risk for a predator to attack a group.
Safety in numbers.
General rule of safety is to travel as a group. Because a group is much bigger threat to the attacker. The group/heard can come to the attacked's defense. If the predator does get a kill the human heard is so very unlikely to let that predator eat the victim in peace.
In other words Attacking a group increases attackers chance of injury and decreases chance of reward compared to targeting an isolated individual. Thus high risk.
History says mega fauna dies.
If you are envisioning larger predator of say T-rex size. Well The best way to take down such predators is with a large group of armed people. History shows that when mega fauna that is inexperienced with humans meets humans... The mega fauna die. In other words predators big enough to be a threat to an army would have long since been hunted to extinction or learned/evolved how to avoid humans.
Presumably marching around in huge columns would be a big target for predators
Eh... no. The only predator that attacks herds is the lion, and they do so only in a very careful fashion and never the herd itself:
Lions sneak between the herd and their prospect victim with at least two lions. Then they attack one after another to drive the separated member away from the protection of the herd and toward other members. They always choose a separated and weak member to attack.
This behavior could be emulated and have some impact: a predator that follows armies and attacks the scouts and messangers.
The predator would change nothing in warfare on a grand scale (army scale) but mandate that scouting be done by several soldiers instead of single persons.
On an intermediate, troop level scale, losses of scouts to the fauna are higher than without, but in general, those losses can and will be attempted to be mitigated. Scouts and Messangers will travel in groups of 4-5 to ensure that the message or report comes through.
At times an army might end up in bad terrain because of losing their scouts, but that is less a presence of the predator but non-adaption of the army problem.
This question is too vague. For a definitive answer, you are going to need to provide much more detail. The answer greatly depends on the properties and capabilities of this "predator", by which I assume you mean a predator of humans.
- How fast can it run? Swim? Fly?
- Where do they live?
- How large and dense is their population?
- How often do they eat?
- Do they have prey other than humans? If so, do they have a preference?
- How smart are they? If they are comparable to human intelligence, no one will be left to fight a war.
In the absence of such specifications, I'm going to provide an answer on the assumption that these predators are comparable to existing apex land predators in our world.
Anywhere they live would probably need to be treated the same as enemy territory by all parties. If it is possible to evade detection by such predators for an extended period, any combat taking place in their habitats would be in the form of guerilla warfare. Even then, fighting is loud, and noise attracts predators, so it may be that combat is entirely impossible. In that case, the regions would simply be treated as impassable.
If it were possible to design some sort of vehicle that is impervious to attack by the predators such that troops could be transported through the region, you may end up with some strange analog for a navy that crosses predator-inhabited regions instead of oceans. Perhaps they might even carry tools and weaponry to cripple enemy vessels, or expose the soldiers inside to the predators outside. However this would likely require technology beyond the medieval era, so it's unlikely unless you are willing to fudge the technological era of your fictional world.
Put simply, man-eating predators would not alter medieval warfare so much as prevent it outright. That may not hold for more recent methods of warfare, but past a certain point advanced technology would turn the predators into prey. The only way for human warfare and human predators to exist in the same place is if humans and their predators were on a somewhat even playing field. However, that puts it closer to inter-species competition than a predator-prey relationship.
Everything would change if humans were not the dominant species. Let’s say the predators are the raptors from Jurassic Park. Smart, strong, fast, great at killing, deadly all around. The biggest change in that situation would be the level of protection each village, town, and house would have. If humans were commonly being hunted and killed, there would be significantly less sprawl. Humans would retreat inside walled cities and towns at night or when the predators were nearby. Populations would be smaller and grow more slowly. Trade caravans would need protection against the predators but not from robbers as nobody would be hiding out in the woods waiting to ambush someone. Expansion into new areas would take time and effort to avoid people being killed. Nobody in their right mind would grab a wagon and just head west to colonize some land. Domestication of animals and the raising of large herds would likely not happen due to losses from attacks. This means that horses, oxen, sheep, pigs, and other similar animals wouldn’t be around to help provide food, clothing, and transportation. There is an increased risk of starvation as food is harder to obtain. This increased level of town security would potentially decrease the effectiveness of warfare since every town would be a fortress. An army would be exposed to repeated attacks while the cities they sieged would be prepared at all times. Supply chains would be at risk of being attacked. Moving goods would take much longer since pack animals would be uncommon or even non-existent. Supplying meat would involve hunting wild game instead of relying on domestic herds. Sending soldiers into the forest to hunt for deer during a campaign would risk losing them. Messages would take significantly longer to arrive since it would take sending a small force as opposed to a single person and nobody would be riding horses. As the wounded piled up, the number of predators would likely increase. Scattering an army would result in a good number of them being killed by the predators if they failed to regroup before nightfall or before being attacked. Armies would travel more slowly as they would need to setup defenses each night to avoid attacks. More troops would be needed to stay awake and guard camps which increases fatigue levels. Diseases would be more likely as latrines would need to be inside camps as opposed to outside. Wars would likely be conducted during winter months when the predators are dormant, which brings up its own difficulties. It would be a snowball effect which impacted every aspect of life.