Some species do, some don’t.
Okay, so that’s a very cryptic answer to what appears to be a simple question. Not unlike other birds we’ve featured, though, a finch MIGHT migrate, but most of the time, they won’t.
Finches are known to be resident birds throughout the whole year; you’ll likely see them just as frequently in the summer as you will in the winter. Their migratory habits are generally decided by their location in the world.
It’s documented that Western finches are perfectly happy at home through the colder seasons, whereas their Eastern counterparts are more likely to migrate south. In some instances, the Western finch will move to lower elevations to evade the cold, though it’s rare for them to travel great distances.
Eastern finches are much more likely to travel thousands of miles to a warmer climate, though it does depend on the availability of their primary food source.
As finches don’t generally eat insects and bugs, they don’t need to drastically change their diet. They may need to change what types of seeds they eat, though luckily, many berries and nuts do grow throughout the winter.