If you take a look at the icon picker's source control, you'll notice that the glyph-icon and font awesome classes are hard coded within the javascript file and there doesn't appear to be a way to put in your own icon set.
I had this challenge a few days ago, and I solved it by using select2 and using it to populate an icon set.
See fiddle: http://jsfiddle.net/m9yLa/2/
HTML:
<select id="icon">
<option value="img1">Img 1</option>
<option value="img2">Img 2</option>
</select>
Javascript:
var formatResult = function (state) {
if (state.id === "profile") return "<img src='img.png' width=48 />";
else return "<img src='img2.png' width=48 />";
};
$('#icon').select2({
formatResult: formatResult,
formatSelection: formatResult,
minimumResultsForSearch: -1,
width: 90
});
CSS:
.select2-choice {
height:60px !important;
width:90px
}