Weather can be a tricky situation at any theme park.
Rain affects very few rides at SDC. Powder Keg and the Galleon will shut down if it rains. Other rides may do so as needed. The reason for shutting down for rain is that the boarding areas and track can become, slick, for a lack of a better word. Once the rain stops and water dries or can be cleaned up the ride will reopen. When extreme amounts of rain fall the cave can become flooded, but I do emphasize extreme.
Lighting affects most of the rides and attractions. Fire in the Hole and the Flooded Mine are able to continue operation. SDC sits on a hill top and is prone to lighting strikes. They take every precaution when it comes to the rides. Once the lightning is out of the area the attractions will do their best to open as soon as possible.
It all depends on the storm that passes through. SDC wants their guests to be happy, so they will do their best to keep the attractions running as long as it is safe. If the storm is small or if it dissipates once it hits Table Rock Lake then your wait should be short. However, if the storm is severe it may be a while before they reopen. If you only have a one day admission and it rains check about the Good Weather Guarantee, if your day is wet they do want you to come back and have fun!