In 2008, at Alpental a friend and I did some on-snow picket testing with skis.
All the tests were done with a 24" MSR Coyote (no cable, just runners), a 10.5mm rope, and the rope was (unrealistically) tied directly to the anchor. Snow conditions were 3-4" of wet corn/slush, and then more consolidated snow below that, on a slope (Sessel) of 15-20 degrees. Speed at impact with anchor felt like ~25 mph(?).
Test 1: Vertical placement, top clip, hammered straight into the snow. Skied 30m of rope. Slight tug on harness, followed by explosive anchor failure, with picket landing ~10 feet from where I stopped downslope, pulling the entire coiled rope with it. FAIL.
Test 2: Vertical placement, top clip, ~15 degrees back from horizontal, placed below slush level. Skied 15m of rope, with the same results as above. FAIL.
Test 3: Vertical placement, middle ("Sierra" style) clip, ~15 degrees from horizontal, below slush level. A slot for the runner was excavated, and then snow was replaced and compacted. Skied 15m of rope. FAIL.
Test 4: Horizontal "deadman" placement, ~2' down, with a trench for runner. 15m of rope skied. Anchor INTACT.
I don't have any way to easily estimate the forces involved, but the forces were all directed down, and should have pulled the anchor deeper in the snowpack, but they simply ripped straight out through the slope.