Reviving an old thread... but there are a couple of ways of brewing with milk.
The first is to use it as a kind of unfermentable sweetener in your brew - specifically, lactose is a sugar that yeast can't ferment. So it can often be used this way in beers, though these days brewers will often not bother doing anything with milk and just buy lactose straight from a brew shop. I use milk in my beers, in the form of whey, which I get from cheesemaking - it's the green liquid that separates from the fatty curds. It's a good ingredient and definitely worth throwing in brews. You could use it as a sweetener, also, in a light dry mead.
The second is to use it in a recipe like a butter beer, which *is* a kind of egg nog made with a sweet beer rather than a fortified wine. The booze is heated over the stove and egg yolks are whisked in with cream. Spices are added. You could do the same with mead to make a sweet dessert or breakfast treat.
The third: the English used to make syllabub, apparently, by directly milking over the top of a barrel of cider! The acidity in the cider caused the cream to curdle: an instant, delightful dessert. Again, you could do the same with mead - and indeed most syllabub recipes are not that precise about what alcohol should be used to cause the cream to curdle.
Fourthly, there are various other ways of fermenting milk; kefir, for instance, is a fermented milk drink that has both bacteria and yeast in it. Villi (from Finland) is another. Skyr probably often had yeast in it as well. Whether the Icelanders sweetened their skyr with mead or honey.... who knows? I don't.
That's all I know! Milk mead sounds a fun project though.