Impossible to say from year to year. The season's first big, cold, pass-choking storm is the key. Often this storm doesn't hit until November, sometimes December, so in those years, the high country remains accessible pretty late. What will 2010 bring? Short days are also a consideration, with fewer hiking hours.
My personal record for a late high-country trip was the weekend before Thanksgiving. There'd been some snow but we slept on dry ground, which was pretty amazing.