I've soaped raw goats' milk and sheep milk, but not raw cows' milk. I did, however, milk a crossbred Angus/Jersey cow for 7 years for raw family consumption, we've also had a herd of Angus beefers in the pasture for 12 years now, and I'm very familiar with the qualities of raw milk. The original post talked about using milk straight from a beef herd, which is what triggered my thought process. Homogenized cows' milk, whether pasteurized or not, would be used like goats' milk because the homogenization would keep it from separating. But unhomogenized cows' milk, whether pasteurized or raw, and whether from beef or dairy cattle, will separate. Chilling hastens the separation since the fats conglomerate faster as they cool. You can see the cream line forming on top within just a few minutes after straining the milk and putting it in the fridge.
I haven't been able to add lye to goats' or sheep milk or buttermilk without freezing it first to avoid carmelizing and burning the milk sugars. But if you stick unhomogenized cows' milk in the freezer, it just hastens the rising and separation of the fats. Logically, you wouldn't add oils or butters to your liquid as you are trying to dissolve your lye, so it only makes sense to separate the milk into its components and add them separately.
If using regular homogenized, pasteurized milk from the store, you can use it without all the hoopla -- commercial whole milk is mixed to average 3-1/2 to 4% fat, and the protein content of Holstein milk is lower than that of Jerseys or any beef cattle. That's within a few points of the "average" goat milk content, depending on diet and lactation cycle, of course. OTOH, when I was milking the Angus/Jersey cross, we averaged nearly a quart of cream out of every gallon and the protein content was high enough that the skimmed milk was still dense and white -- not watery and blue. You can imagine what that did to DH's cholesterol! Wish I had that kind of time and energy again.