LAKE PLACID, N.Y. — Some nights, it is so cold that not even those who live here venture outside, so the Palace Theater closes early rather than show movies to an empty house.

But single-digit temperatures are the least of the challenges facing this 87-year-old theater. The Palace, like many other small-town, independently owned theaters, is struggling to comply with an industry-imposed transition from 35-millimeter film to digital.

“People come in and say, ‘You can’t let this go dark,’ ” said Reginald Clark, 84, who owns the theater with his wife, Barbara.

It costs about $65,000 to alter each of the theater’s four screens, primarily for new digital projection equipment. The people of Lake Placid — much like the citizens of Bedford Falls in the film “It’s a Wonderful Life” — have come to the Palace’s defense: Community donations enabled the conversion of one of the screens to digital. Mr. Clark’s extended family pitched in to convert another screen.