You use CSS in the same way, just with the home page body class. For example:
.home .sprocket-mosaic-item .sprocket-mosaic-image {width: 60%;position: relative;z-index: -1;}
That code will work in most cases, but it depends on how your site is set up. Use a web inspector to find a body class for the page.
Also, Widget Logic is not a good choice for Gantry, since we have the page override system built in it is unnecessary and causes conflicts in some cases.