Stef has asked about information on Denmark in English , I have provided some information here which may be of interest to others as well
There are many forests in Denmark where a family could go . The best place to obtain information would be the Tourist Information centres who I have always found very helpful and you will find many brochures in English as well as other languages, especially German.
The Visit Denmark site is perhaps the best general starting point.
With regard to the forests, there are some English pamphlets for various forests and these can be found here We can recommend Jægersborg Deer Park as well as the white chalk cliffs of Møns Klint and closer to Copenhagen Stevns Klint. Stevns Klint is accessible from Rødvig Railway station, an approx 2 hour trip from Copenhagen.
Getting around in Denmark on the public transport system is easy and the system is reliable. Using Rejseplanen (available in English here) you can find the times for buses and trains for most cities, towns and hamlets in Denmark.
Finding where places are can be a problem, so we suggest you use the internet mapping system known as krak.dk, whilst not in English if you select the tab labeled Kort and type the name of the township into the Postnr./By space in most case that will give a map of the area. However, Google Earth is also an alternative.
The Danish Weather Service forecasts are available in English, they provide a 5 day outlook for all regions.
We hope that this information is helpful