You will be fine. There is SO MUCH to do inside. We went for our honeymoon duing a "small" hurricane. I was so sad, but actually, it worked out for the best. The park was not so crowded and my hubby and I had fun playing in the rain. It rained in the morning and then we went back to our room after a few rides, took a nap and by the afternoon, it was blue skies. It won't rain long there - and most of the rides are inside, so they won't close. Just have fun, it is what you make it. You are at the happiest place on earth.
Have fun and don't panic. It will be GREAT.