I’ve had enough of the problem. Just a minute ago the app was updated but still the icon is invisible in dark mode of the Yosemite. It was just a quik dive into the app content and replacing the icon. I’ve changed the original one by replacing the color (black to grey). That’s enough for me as I’m too lazy doing someone elses job. I’m not bothered by the other states of the app. All I need is to see the app is running. The file you’re after is StatusIcon_signedin.tiff. So there you go:
Update: Skydrive application is updated and fixed the problem.