I want to give a specific atmosphere to the chapter. Sort of a
whimsical, medieval festival-like atmosphere. However, they lack the
ability for a lot of modern festival things, such as music and
dancing, outfits, etc.
Animals make music.
If these animals live in a forest, they hear birds singing all day long, they couldn't escape it. They would all be aware of daily 'music' even if they don't vocalize themselves.
Foxes make enthusiastic trills, and barks, and dog-like woos. Not sure what badgers and raccoons sound like, but there are internet videos of a porcupine 'talking' while he eats. Male mice sing to female mice for courtship – above the human range of hearing.
As for outfits, animal fur and feathers change throughout the year. It's not clear when your festival takes place (at the begining or end of winter). You can describe animals as being more attractive with their hibernation weight, or their winter coat, or whatever sounds logical for animals to look like this time of year.
worldbuild it
You've already created a society and a festival. You only need a bit of author confidence to create their festival songs – what you need is an angle, something to make it interesting and a bit of worldbuilding.
Not all species are equally good at singing and dancing, they'd have their own versions that suit their bodies. They may have some pride in their own traditions, with similar traditions in near species who share the same ecosystem,and some won't quite 'get' the quirks of the other animals' traditional festivities.
Children may find plenty in common through play, even species that are only close in height for a short time while the adults rarely mix.
Characterize it
Individualize specific characters that are universally recognized. An old man with the longest whiskers, a fussy woman who needs to control the food presentation, someone who sings a little too loud. Think back to every state fair and extended family function, add some of those touches.
With this comes some technology, such as spears, clay molded to make
some form of bowls, fire, satchels, etc.
If they have bowls and sewing, they have drums. With spears, they have reeds and woodblocks and maybe wooden chimes or other tuned percussion. It doesn't take advanced technology to bang two things together and make a sound.
I get not wanting to Fred Flintstone an entire civilization, but all societies have members who work seriously while other persons entertain. If a technology can be used in practical ways, it can be adapted to help pass a winter underground.
Give it stakes
An entertainer of a forage-and-storage clan might actually earn their keep through the lean months. 'Bards' would use the festivals to network, share material, and publicly perform to make their reputations and gather invitations for wintering in a prominent clan's burrow.
The whole festival could gain a new dimension if a character has stakes in maneuvering its social aspects. Give them something they want and something they could lose, and then make the situation more complicated than they'd anticipated.