Winter is the biggest reason I'm going to miss the mining. In Friends of Mineral Town for the GBA, my personal pick for best game in the series, there was even a second mine with more valuable stuff in it that could only be accessed in the winter by crossing over a frozen lake.
EDIT: Evan, you do know that you can buy extra feed from the animal shop if you need it, right? It's expensive, but if you need it it's there.