Converting graphics?

[ffutures]

I've been trying to work out the best way to handle the Army and Navy Stores files without losing resolution or messing up the images. I suddenly realised that out of habit I've saved them all with 256 grey scales, but there is no apparent loss of quality at 16 grey scales and files are less than half the size.

Given the number of files I really don't want to load them, reduce the number of colours, and save them again manually. Can anyone recommend a program (preferably for Windows) that'll do this for all the gif files in a directory?

Now sorted, thanks to nojay who recced Irfanview Files have been converted and uploaded already, really can't see any difference except speed is better and less space is used.