I was here in the middle of summer, but ended up having to buy an umbrella (or I'd get soaked). Just buy a little umbrella that folds up neatly and won't take up much room in your bag. As always - dress in layers so you don't have to carry around a bulky jacket or jumper with you. Add to that, comfortable shoes for walking that suite all weather types and you will be fine.
Photo Equipment: Stockholm is stunning at night, the lights reflecting off the water - amazing! So just make sure you have a camera that takes night shots.