No good oppotunities close. There is an indoor ski center in the suburb Roedovre http://www.isgk.dk/ or you might try this possibility 110 km from Copenhagen (in Sweden) http://www.vallasen.se/. I have not tried any of these possibillities myself though. almost 8 years ago
One little fact about Denmark. The are NO mountains,,, not 1! In fact the tallest peak in Denmark is called "heaven/sky mountain" and is technically classified as a hill!
Danes go to Sweden, Norway and The Alps to go skiing, and the skiing is good there. In fact, Denmark only gets a light sprinkle of snow (by most ski area standards)... The last two years this has not been the case, however, there are still no out-door ski resorts inside Denmark. The nearest is an area on the Swedish/Norwegian border, the name slips me by. I'm sure I read someone before me had mentioned it. I've heard it is a party area and can get "crazy-with-snowboarders"... If you are with family and children I recommend places in Norway, such as Lillehammer (host to the 1994 Olympic winter games)... Where prices are not as inflated as The Alps (Switzerland, France Italy, Austria)
Sorry to burst your 'snow' bubble! ;) almost 8 years ago