I have never been on a ski holiday and certainly not in the Italian Alpine region. Heiße Oma is a hot alcoholic drink which is only known in the Italian Alps (as far as I know). The alcohol is provided by bombardino an Italian liquor which consists of eggnog and brandy (or rum).
To make Heiße Oma (2 mugs) heat 500 ml milk (don't boil).
Add a package of vanilla sugar.
Add 125 ml bombardino (or a bit more).
Heat and mix.