Still, window shutters were standard on the cottage and revival homes of the period, especially Dutch Colonials and Storybook houses. And they were also found on some bungalow variants.
Consider shutters if they are common in your region, and if you find evidence of their use. (Hardware or holes may remain around the windows; you may even find the old shutters stuffed in the attic eaves.) If the house has English or European pretensions, it may have had shutters. Dutch Colonials often had brightly painted “cutout” shutters, with a motif cut out of a solid panel. Storybook houses tend to feature everything on the facade, shutters included.
And any house transitioning to the Colonial Revival may have had shutters when it was built. This is true of Foursquares and Shingle Style houses, as well as more academic revivals, like Georgian or Federal Revival homes.
My own house was built in 1904 with two quite different facades. The street front is Tudor-leaning English Arts & Crafts and features paired windows and bays—no shutters. But with six-over-one windows, the rear is more Colonial Revival, and it did once have shutters. (The originals are still stored in my attic.) That side faces the ocean and its storms, so these shutters may have been more than decorative, even in the 20th century.