If this was a RWD car, your mother would be correct, as long as the weight was placed directly over the rear axle. Placing the weight in the extreme rear of the trunk would actually produce a “pendulum effect” on a slippery surface.
That being said, a FWD car has no need for weight in the trunk, and in fact, this would disturb the normal weight distribution and actually lessen front wheel traction. As Mr. Meehan stated, the best bet for improved snow and ice traction in any vehicle is a set of 4 modern winter tires.