Burying dead fish, especially large specimens, either for fertilizing outdoor plants or to just recycle the nutrients naturally, isn't a bad idea but it's obviously tougher to do when they die in the middle of winter. I have buried dead fish in the Springtime around rose bushes. They take time to break down so the effect is not immediate but they do seem to help. Just one word of caution from experience... bury 'em deep enough the neighbors' dogs don't try to dig 'em up!

This time of year it's probably easier to wrap the dead fish in old newspaper and put it in the trash.