Yes. The easiest way is to simply replace the original "close" icon with yours (ie change the name of your image and put it in the assets/snippets/ajaxSearch/images folder).
The harder way is to hack the javascript to use your icon instead of the one it uses. I’ve done it, although I’m not all that great at javascript. It’s line 60 of the assets/snippets/ajaxSearch/js/ajaxSearch.js file.
var c = new Element('img'); //Close Image
c.setProperties({
src: _base + 'images/cross.png',
alt: 'close search',
id: 'searchClose'
});
c.addEvent('click', function(){closeSearch();});
By the way, that’s turning into a really professional-looking site! There’s a typo in the last paragraph of your privacy policy, though.
☆ A M B ☆
And I’ll fix that typo likely sometime today, when I update next.