Wouldn't the handbrake only help if your hanging the wheel the brake is on? And on that point, which side has the handbrake?
Ever driven with the handbrake up? Most of us have at one point or another - and yes - the handbrake will affect both wheels, BUT, it will DEFINITELY slow the wheel that's in the air, or spinning in the slush, causing the differential to transmit some power to the one that's still on the ground, or hopefully has more traction.
How effective it is really depends on the nature of the terrain, but sometimes all you need is a few inches of movement.