I do not know about cows' heredity, nor whether there are alleles for patches even in single-colour cows. If there are, this would explain it. If all the patches were coloured white, the cow would be all white, but offspring could still be particoloured.
This certainly happens with cats. An all-black cat still has tabby alleles, and (in certain lights) you can see slightly different shades of black, arranged in tabby stripes.
With people it's different. All races are self-coloured. Skin colour, like hair-colour or eye colour is controlled by genes.
Now imagine (it's more complicated. but this will do for a start) that only one gene controls skin colour. A mixed-race couple (pure black, pure white) reproduce. Since black is dominant and white recessive, the white gene will not influence the colour; it is dominated by the black, and all offspring are pure black.
If these offspring now reproduce with other interracial people, all those having a black gene (from either father or mother) will be black, regardless of the other gene. Those who get WW (the same from both parents) will be white.
In fact there is a range of genes influencing skin colour. In each pair, black (we really ought to say, dark brown, since the blend as we shall see is not grey but a lighter brown) is dominant. In a 2nd generation pairing not all of these pairs in a given coupling will have a B gene: some will contribute WW to lighten the mix. Hence the range of skin colours in children of the same couple.
It is possible, then, for a mixed-race couple to produce children ranging from dead black to dead white, though these extremes are rare. And to further complicate things, there is probably no such thing as a pure black or pure white person: even a blonde from Finland probably has some melanin (black skin colouring) producing genes, and even a black, black African might have a few white genes. Hence some degree of mixing occurs even in the first generation, though the children of these unions tend to be on the dark side.
Something of the same sort also happens with hair and eye colour.