Have you got Adobe Photoshop or Elements?
There's a neat tool called Shadow/Highlight which would help lift the brightness of the frame. The detail currentty 'hidden' in the dark areas does depend greatly on the quality of the camera sensor though.
Try having flash override on or your other option is a bit more involved & requires taking 2 photos of the subject - 1 exposure correct for the bright snow & 1 longer exposure for the shadows then merge the 2.
Hope this helps