Winter temperatures have been increasing across the northern parts of the United States and will continue to warm over the next several years, which will cause shorter winters. Warmer winters mean more pesky bugs, which are already expanding further north. Warmer temperatures lead to less frequent hard frosts/freezes, causing these pests to stick around longer into the winter season. Ticks are responsible for carrying Lyme Disease and are projected to expand across the US as winters get warmer. Warmer winters also lead to longer survival of beetle larvae. The Pine Bark Beetles are responsible for millions of pine forests destroyed across the western US, Alaska, and Canada due to infestations in recent years.
Opposite of mild winters are brutally cold winters. It can be miserable for some wildlife species, but most animals are very good at adapting to colder climates and have evolved over the years, especially those living near the poles. An example is the Arctic foxes and canine species. These foxes have frostbite-proof feet and the canine's fur grows very thick during the cold months. Some animals find a way to conserve energy, such as hibernating or have thick layers of fat. Others simply pick up and leave, migrating to warmer climates. As mentioned, most birds migrate during the cold season, but some birds will seek out shelter that is either natural or man-made during very cold days and nights. An example is the flying squirrels who cram into small holes in trees or cuddle together to stay warm.
With climate change, some species have already expanded into areas and when a cold snap occurs; they are not prepared. A few examples of these animals, starting with the Carolina Wren. They have been expanding northward over the past decades. These birds do not migrate, therefore, during very cold snaps, some of them end up dying. In the years with very cold weather, the Wren sightings have diminished, but the good news is their population regrows and expands north again. Next, the Virginia Opossum. Again, they have been retreating north and these animals do not have fur on their ears or tails, making them susceptible to frostbite during harsh conditions. Last is the Manatee, who need tropical environments and warm waters to live. If waters get below 68 degrees F, they suffer from what is known as a "manatee cold stress syndrome," which leads to starvation and death.
Again, most wildlife adapt to cold temperatures and have evolved over the years to live in colder climates. So when the weather turns cold and nasty, it is comforting to know most of them are staying warm.