In front-wheel drive, does parking brake securear wheels?

Thanks VD and MC.
When parking on a sloped snow or ice slippery road, I claimed (assumed) that we should also engage the parking brake in case the front wheelslide.

Years ago, while sweeping chimneys, I parked my Toyota Corolla Station Wagon on a customer’s sloped snow-covered driveway so that the back bumper would keep my fully extended extension ladder from sliding out.
On the chimney I heard a sound and saw thathe Toyota slid into the street.
Stranded, I had carefully find my down from the 2nd story roof by another means.