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정동진시간박물관 · Gangwon
Open all year round, according to the official listing.

Photos: Korea Tourism Organization (KOGL Type1), shown unaltered.
Jeongdongjin Time Museum is comprised of a steam locomotive and 180-meter-long train at the famous Sandglass Park. It features interesting and unique exhibition spaces based on the concept of time. Since its opening in 2013, the museum has been introduced on Korea's major television channels as well as Chinese TV programs.
Source: Korea Tourism Organization open API (modified listing as published). Hours can change without notice — please check the official website or call before visiting.