You can usually find winter squash in the summer, but winter squash such as acorn, butternut, spaghetti squash, pumpkin are best in the fall and winter months. These squash are allowed to mature until their flesh is thick and shells are hard, so they require longer cooking times than summer squash.
Because they have such thick skins, you can store whole winter squash for a month or more in a cool, dark place, not in the refrigerator. If it's cut, you can refrigerate the squash for about a week in an airtight container in the refrigerator.
Recipe: Roasted Winter Squash