Given a transparent PNG displaying a simple shape in white, is it possible to somehow change the color of this through CSS? Some kind of overlay or what not?
To literally change the color, you could incorporate a CSS transition with a -webkit-filter where when something happens you would invoke the -webkit-filter of your choice. For example:
img {
-webkit-filter:grayscale(0%);
transition: -webkit-filter .3s linear;
}
img:hover
{
-webkit-filter:grayscale(75%);
}