Animated .gif is special case because it has multiple frames (or images). Software is sparse because flash just about killed it's usefulness. I *think* Gimp may be able to work with animated gif's. Other options might include video software that can output .gif animations which might be your best option, should be able to open, edit and save with Virtualdub but I'm not sure
Photoshop has a component called image ready that works with animated gif's but I don;t think that comes included anymore.. Only other viable commercial solution I'm aware of is Uleads Gif animator but that is no longer made. It used to come included in Photoimpact but I don't know if that is still the case.
Reducing the filesize can include any of the following. Reduce the dimensions, amount of frames or color palette. Reducing the frames or color palette can have undesirable result depending on what you are working with.
If it's just one animation shoot me a sticky email with link and I'll do it for you. Only take a few seconds but i already have the needed software.
Gamani have some software that can optimize gifs. However - a better format would be APNG (also supported by this software), which has smaller file sizes anyway (as well as being able to handle millions of colors, and alpha transparency).