It is partially possible
In HTML5 you are not able to change the style of the ghost object
but you are able to change the default ghost object with the
setDragImage method from the DataTransfer object.
Made an example here (the blu div will become a red div when dragged):
<style>
#div1{
background-color:blue;
width:100px;
height:100px;
}
#div2{
background-color:red;
width:100px;
height:100px;
}
</style>
...
<div id="div1" draggable="true" ></div>
<br/>
<div id="div2" ></div>
<script>
document.getElementById('div1').addEventListener('dragstart', function(event) {
event.dataTransfer.setDragImage(document.getElementById('div2'),50,50);
});
</script>
http://jsfiddle.net/ftX3C/
So you can't change the style, but have a hidden element from which to use as a ghost image. It can also be an img or a canvas.
I recommend the following tutorial about html5 drag and drop:
http://www.html5rocks.com/en/tutorials/dnd/basics/
also read about the DataTransfer object after you finish that tut:
developer.mozilla.org/en-US/docs/Web/API/DataTransfer