POULTNEY, Vt.—As Green Mountain College readied to close its doors after 185 years, students enjoyed one of their final spring days on the pastoral campus, with some carrying kale and cabbage from the school’s organic farm and others preparing for a class camping trip.

The school, along with two other small colleges in Vermont, will hold its final commencement this weekend. Green Mountain President Bob Allen mourned his college’s demise as well as its impact on an aging state that is struggling to hold on to young people....