If it is just raining with no lightening, most of the rides keep operating. Yesterday, during Colin, the water rides and Dragon Challenge were running. My daughter did 2 rounds in the front row of DC. She got soaked and said it felt like bees hitting her face.
But yes, lightening will shut down quite a few rides at IOA. Doom's, Blutos, Dudley, pteranodon flyers, Jurassic Park River Adventure, Hippogriff, Dragon Challenge, High In The Sky Seuss Trolley, and One Fish, Two Fish all close when lightening is near.
Over at the studios, Hollywood Rip Ride Rockit, Woody's Nut House Coaster, and Kang and Kodo's Twirl n Hurl are the only things that close.