So, I think I’m missing part of what you mean, but I saw some elements to clarify.
Facing off against Animals: (Natural Order, Pg 221)
So first, allow me to simplify the ways mice (whether Guard members, settlement mice, or wild mice) interact with animals. I say there is Livestock & Vermin, Enemies & Predators, and Scavengers & Migrants, with a few Monsters & Gods.
Livestock & Vermin are insects, arachnids, little fish, maybe moles, shrews, bats, frogs, toads, newts, salamanders, small snakes and insect-hunter snakes; I think hares, rabbits, medium (non-raptor) birds and small birds, are livestock and/or vermin. So these are animals the mice use or work against. In the case of livestock, they are managing these animals for beneficial purposes, so like having a silk farm of either silk worms or spiders could be a typical career among settlement mice. We know the Guard has a beehive with honeybees. A hive of ants or termites might be a food livestock or a trained construction livestock. Small fish might be food or used as bait for other things. Now, this means animals which are attracted to these livestock sources or the other food sources of mice, yet are not predatory towards mice, are vermin. So, that’s why to list frogs, toads, snakes, bats, moles, shrews, newts, salamanders, birds, and insects or arachnids as vermin–they try to get at the livestock of mice! So, the mice need to actively work against infiltration of these vermin. It could also include mites, lice, ticks, mosquitoes, fruit flies, fungus gnats, etc. as vermin that are a nuisance to mice. Ok, so that’s the simplest terms of Livestock & Vermin. Oh, the hares, rabbits, birds could be transport animals just as we use horses, that makes those livestock.
Enemies & Predators are weasels, minks, ferrets, fishers or martens, sables, and the many predatory animals listed such as fox, wolf, owl, hawk, falcon, coyote, flying squirrel, snake, shrike, etc. This fills two roles. The enemies can be treated like civilized, although antagonistic, NPCs who conversate, negotiate, manipulate or persuade, and otherwise interact. No every campaign has to treat these as kill-on-sight, but that is a frequent outlook. Just keep in mind these enemies are interested in using mice–these are not competitors. They have an interest in eating mice, making mice work for them, stealing from mice, and possibly holding mice as livestock. Predators are fairly similar in the desire to eat mice or capture for later eating, but don’t have the established civilization; I very rarely want the players treating the predators as something to talk with, but I always allow a Loremouse test to provide some rudimentary exchange of intent without a full conversation. Like, I’ll never have players using a Speech conflict among predators, but I’d allow a Negotiation conflict if they think there’s an exchange to be made. Ok, that’s the simplest way to look at Enemies & Predators–they want to eat mice, capture mice, or otherwise kill mice, rather than steal food, lands & burrows, or cultural pieces. Well, I guess maybe weasels and their cousins might be trying to steal burrows and lands and cultural elements, even scientific research. That’s a bit fluid based on the campaign.
Scavengers & Migrants are porcupine, badger, whistle-pig or woodchuck, otter, raccoon, skunk, deer, crows, ravens, vultures, and many birds which migrate such as ducks, geese, herons, and various song birds. Mostly, these animals don’t actively seek out mice as food, but many are willing to eat mice when there is opportunity. So, badger, skunk, otter, are examples of scavengers that would take a swipe for a mouse if there is a chance, but they aren’t going about stalking mice. Heron is a bird example of the same. Other effects of the scavengers is they will destroy livestock, grazing they’ll sift trash pits and granaries or storehouses. Especially enjoyable is the penchant for mischief from raccoons, crows, and songbirds. In addition, the deer lies near the line of Monsters & Gods; a buck in rut could cause immense damage–thought not maliciously–in mouse terrain such as trees, burrows, fields. Most migrants are grazers that can overwhelm a food source terrain where mice frequently harvest. Ok, that’s a simple view on Scavengers & Migrants.
Monsters & Gods are bear, moose, wolf, wolverine, and deer, maybe includes eagle, condor, albatross, flocks of geese, hordes of locusts, schools of fish such as sardines. These are the forces of such size that mice barely get noticed against their footprint and rarely can take action against them and their presence. These are very rarely seeking to hunt mice, but will use opportunity if possible. They are just so big compared to mice that even a lite snack is a massive mouse storehouse of wild fare. These rarely interact directly with mice and could barely be influenced by mice.
So, that’s a simplified view of the animals. Now, let’s look at the Natural Order bullets to simplify the ways that mice might interact in tests or conflicts with animals.
First, Killing: mice could kill other animals whether with weapons, traps, snares, nets, knots & bindings, teeth, paws, claws, or whatever. That’s specifically using Fighter or Hunter.
Next, Capture, Injure, Run Off: specifically using Fighter or Hunter mice could capture animals, cause injury, or drive the animal(s) away.
Finally, kill, injure, trap using Scientist or Militarist.
All of these relate to the natural order ranking; if you look at natural order and Nature rating, most of the Livestock & Vermin, some Scavengers & Migrants, and Enemies are approximately in range for mice to handle capture, injure, drive off, or kill. Clearly dealing with livestock is an area in which killing is simple; dealing with enemies and small scavengers is a challenge. Dealing with larger scavengers, predators, and large migrants in restricted to only driving away. At least by Fighter and Hunter tests or conflicts.
When looking at Scientist and Militarist tests and conflicts, then you can begin to face off against medium and large animals of all types and can engage in killing, trapping, injuring as desired.
The Natural Order table shows that most of the high Nature ratings are above mice and above by multiple ranks–which gives clues about developing invented animals not listed in the text–and that restricts how a group of mice or a single mouse can interact with those animals. A patrol of three or four cannot really deal with a bear effectively in any way without using Scientist or Militarist (which indicates a large group of mice being rallied to assist). A patrol could probably deal with foxes and lesser best via Scientist or Militarist (still indicates a group of volunteers), but alone could do little more than drive off using Fighter or Hunter tactics.
I’ve left some animals out of my descriptions, but you can probably figure a space for those.
The next thing to consider is how animals interact with mice. The livestock, vermin, enemies, and predators have a fairly one-to-one relationship with mice and have face-to-face encounters which may lead to major conflicts. The scavengers, migrants and more would typically ignore mice or see them as a nameless, faceless wild creature.
anyways, the shortest answers is, Yes, a patrol or larger group is meant to challenge even large animals. The additional notice is that they should be facing larger animals with Scientist or Militarist and should be prepared for a massive challenge with very limited results (in other words a significant compromise and sacrifice of effort, time, energy, resources, and training). As for how often they can expect to reach their goal, that will depend on the goal, the skills, the dice, and the investment of resources like Fate, Persona, Gear, and Traits. But, another look at that is to say that PC mice are generally getting Success, Success w/ Conditions, or Twist. Even the results of Conflict & Compromise should roughly appear to be Success, Success w/ Conditions or Twist–but with more nuance and variety.