It is not dangerous but can upset there stomachs, I would recommend goats milk rather than cows. You can also buy special milk for dogs from your local pet shop.
If you give your dog milk.....you can always water it down a little.We give our old girl milk and water(warm) after each breakfast and tea and she loves it.We have always done so and they have never had any bad reactions to it,but as first answer said you can always buy goats milk.Regards.
There is no need for your GSD or any other dog to drink milk unless it is a puppy!
Just given them water. It is all they need.
You are more likely to have problems by giving them things they would not "normally" have - and GSD's are a breed particularly noted for having skin/digesting/allergy problems and milk is a common culprit in these.