The Weather always seems to schedule a downpour for us when we're in Epcot.
Be aware that the concrete sidewalk which links WS becomes VERY slick in puddles. My DS was in rubber soled sneakers, and my DD was in flip flops and both of them slipped and took headers. (then DS discovered he could get a heelys effect w/out the heelys by hydroplaning along on his slick soles. fortunately the rain had been so heavy that great expanses of sidewalks were vacant. Yes...we shut him down real fast.

)
DD could only stay upright by holding on to both me and my hubby. She finally took off the flipflops and just went barefoot.
What was amazing to watch at Epcot -- and I am talking a torrential downppour here, before we were contending with the puddles and slick sidewalks in WS -- is that there was basically a foot deep torrent surging along on the main sidewalk in FW. It had been cloudy but no drizzles when we went in to watch HISTK.
We came out to discover the sky had opened, and it was beyond pouring. The worst rain I've ever seen. In the only time I've ever reported CMs, a couple of teenage ones were demanding that all the guests, including those with no ponchos and very small children, leave the awning and go out into the rain. But there was a river....fast enough to sweep away a child...out on the sidewalk.
Several men appeared, moved trashcans, and opened up drains I'd never seen before. All of the water almost immediately flowed down the drains and the river was gone. It was amazing. The CMs still made everyone walk out into the rain, while they stood there all cozy in their jackets. There wasn't even another show going on.