Yes, EPCOT remains open during rain, and it is often considered the best Disney park to visit on a rainy day because the vast majority of its attractions are located indoors. Massive pavilions like The Land, The Seas with Nemo & Friends, and the Imagination! pavilion offer hours of entertainment under one roof. Even the World Showcase features many indoor films, exhibits, and large dining halls that provide excellent shelter. While outdoor entertainment like certain live music or character "cavalcades" may be delayed or moved, the rides themselves (like Remy’s Ratatouille Adventure or Frozen Ever After) continue to operate as their queues and ride tracks are fully enclosed. The only major exception is if there is lightning in the area, which will cause the suspension of outdoor transport like the Friendship Boats and the Skyliner. If you are prepared with a poncho, a rainy day at EPCOT often means significantly lower crowds and shorter wait times for the most popular "heavy hitter" attractions.