I got this filter on a lens i won off e-bay and im not sure what ide use it for. What is skylight filtering even doing other then changing the tone of the image.
I recently got a Hoya Skylight 1B as well (but then you already knew that). Skylight filters are "designed to warm the image a bit by removing some blue light along with the UV" (from dpFWIW), so I'm actually rather perplexed as to why your image with the filter on the left appears more bluish.
Anyway I've never noticed any difference with my Skylight, so I just use it to protect the lens and zoom mechanism when I'm out somewhere dusty or sandy.