Just a debate I’m having over what MATERIAL the cloaks would be made from? Fur of small animals? Some sort of leather? Often cloaks are wool but where would mice have access to wool? So plant fibers maybe similar to cotton? Maybe getting to specific but just curious. This MAY be because my group has interest in moving towards a LARP.
What I made up is that the cloaks are made out of linen. Plant based fiber (flax plant) and I checked it can grow in Michigan. Plus many people in the Middle Ages wore clothes made out of linen.
Another thing I thought about is that the mice of the Guard are really recognizable thanks to their cloaks, perhaps it is because they are made out of wool. One can imagine that while the mice go out to maintain the scent border, they can come across some sheep’s wool that has fallen off or a little bit that got pulled off because of some bushes (mice won’t need much wool). Then they take it back to Lockhaven where they have a renown weaver. This could make wool a rare commodity, really sought out after in the Territories and explains why the cloaks stand out so much.
Just some ideas for you… 
I like flax/linen! but I wonder what other non-sheep wools there are out there? There must be an equivalent.
I had invented a story of Wolfepointe mice who gather the shedding of wolf winter fur during spring and use that for making wolf wool.
My ideas:
In addition to linen, other plants used for weaving cloth are nettle or hemp. Both were used in the Middle Ages, nettle was the equivalent of cotton as it is soft and flexible, whereas hemp is a bit rougher and less delicate.
Furthermore, I thought about the “problem” of the material being water-resistant, and I came up with the idea that they could use the beeswax from their apiaries. Apparently this was used for a long time, the beeswax is molded in the size of a bar of soap and then scrubbed on the textile and it becomes water-resistant.
In addition, the mice have access to birds (either birds they befriend or birds as adversaries) and we still use down as isolation. I suppose mice could use feathers as well…
What about rabbits or hares? The mice sometimes mount hares which can shed. I guess a fancy angora cloak for ceremonies could be possible.
Finally, I was thinking about silk… Some beetles or bees can produce silk. I don’t know if the mice would have caterpillars which make cocoons out of silk since they do eat a lot and could attack the plants that the mice are trying to cultivate?
But mice fight against spiders and spider’s web is a sort of silk that I suppose the mice could have learned to weave.
As for finding an equivalent for wool, I think that hemp would be the closest (that I know of), but it’s really hard to find an equivalent because the wool fiber is quite particular: it’s not smooth like most other fibers which is what makes it great for isolation and staying warm. I’m certain there could be other plants, but we have been relying on wool for such a long time (around 1600 BC) that I don’t know if we (humans) have studied all the other possibilities…
I like the idea of the wolf wool. Could be a nice scenario, but dangerous one as well.
This is what I love about RPGs, you start asking yourself improbable questions like “hum, I wonder what talking mice in the Middle Ages would wear”
I once made a town in Mouse Guard that had made a deal with a Spider for use of its silk for cloaks and things, while they got its food.