Some of the best times I've had at WDW were on days it rained all day. On days like that, the rain usually isn't heavy, just continuous gentle rain.
One time was in the early evening at Epcot, on the very first day that Tapestry of Nations ever ran (technically, I think it was the first preview running, an the official "opening" was a few days later). It was in October. There was a steady drizzle, but it was not too cold. We started with ponchos, but they were a bit too confining and made us sweat, so we just took them off and danced in the rain with the big tall stick figures. Camera crews were out filming for promotional footage, and they filmed my then 6 yo daughter a lot, because she was just really adorable dancing around in the rain (EIIDSSM). It's probably my fondest WDW memory. The rain let up enough to show Illuminations ROE, which blew us away (it was our first time).
Another time I'm reminded of (and I know the OP asked about "rains all day" and so this is a bit OT) was when we rode Splash the first time. It was a beautiful sunny day when we went on and rode the outside part. When we were on the inside part, a huge storm came over, and when we got to the drop, we thought that the downpour was some kind of effect! :lol: It wasn't until after a few seconds after we hit the bottom that we realized that it was pouring (remember - it was the first time ever that we rode)! We bought ponchos and walked around in them for a while, but the storm didn't last long. A lot of people left and the rest of the day was a pleasure because of the short lines.
One last comment: I find that wearing lightweight wool socks helps if it rains. They don't hold the water much and dry very quickly. I wear them with every kind of footwear, and even if your shoes are wet, the wool socks makes it more comfortable. Once cotton socks get even a little wet, it is very uncomfortable, they'll never dry, and could cause serious blistering.
P.S., one day when it was raining all day, it was way too hot for ponchos, we just put them away and walked in the rain. Oddly, we put our ponchos on when we went inside because we needed them to keep warm in the air conditioning with soaking wet clothes! We had a great time, though!