Someone told me it saves money to buy wine, spirits, etc., at the Duty-Free shop as you enter Denmark so you can have a drink in your room before going to dinner, saving the cost of buying wine with your meal. Does anyone have information about this? How much can one person bring in with them?
You are in error how duty free works. Our experience is that the duty free shop will ask to see you departing boarding pass. Since you don't have one you can not purchase. You can always buy at a local shop because that will be cheaper than buying at dinner.
There is also a duty free shop by the baggage claim just before you exit the airport, but I have never found it to be cheaper than what you can get in regular supermarkets. Most supermakets have weekly deals that are cheaper than what you can get in the duty free anyway.
Frank - some airports do have duty free on arrival. The only one I personally remember is Rio de Janeiro, but it appears Copenhagen is another one.
Whether duty free shop prices are a good deal is a separate issue.
You may also be able to buy at your departure airport. Once past security you just need to show your boarding pass at the duty free shop and they will deliver your item(s) to the jetway as you get on the plane. We found out about this at JFK when traveling on St. Patrick's Day and succumbing to the free samples of Irish whiskey.
It won't be Duty Free unless you are entering directly from a country not in the same Customs area, that is you can't save Duty from anywhere in the EU.
You have to get the Duty Free at the originating country, not the country you are arriving in, and unless you get it from the airside duty free shop you won't be able to take it on board.