It would be a sad story if you have the writing chops. Waiting for winter to end has been a human preoccupation for as long as humans have lived in the north. They would be waiting for a spring that never comes.
In the north, plants power down, big animals live on their reserves and little animal hibernate.
Deer go into the winter with a full tank of gas (fat reserves) not
knowing how long the journey will be. If deep snow and bitter winds
start early or persist late into spring, some deer will run out of gas
(fat reserves) and die. The greatest mortality is experienced by
fawns, followed by adult bucks and then does. Severe winters can
significantly deplete the fawn crop, resulting in drastically reduced
recruitment into the population.
Your story would start in April. Days would get longer, but not warmer. Starving deer and rabbits eat the bark off of trees when they are hungry. Dead deer would start to turn up. Then animals like squirrels would come out of hibernation and die. A bear could come out and start eating the frozen dead deer lying around. Deer (and I think rabbits) will eat meat if they can and I can imagine a cannibalism scene with the deer. They do not have the right kind of teeth or jaws for frozen meat and they would struggle.
The birds would not come back.
If this is inland and it never gets warm enough for the plants to grow, all of the animals will be dead or moved on within a year.
You could have the humans save one squirrel. They could go out and clear off the snow and ice so it can dig for the nuts it hid in the fall. It would be pointless, but everything is pointless.