A little way outside the city to the north is a suburb called Klampenborg, which can be reached S-train, or by a very pleasant 10-15km cycle up the coast. It is best known for being the main entrance to Dyrehaven (The Deer Garden) forest park, one of the most popular recreation areas for Copenhagen city dwellers.
Jægersborg Dyrehave is noted for, obviously, it's population of deer, and it's ancient oak trees. It's a lovely place to visit for a picnic, and you can spend several hours walking or cycling the many paths.
It is also home to 'Dyrehavsbakken', but that's for another tip...
North of Copenhagen there is a large forest made by king Frederik d. III in 1669 for the purpose of parforcehunting (riding to hounds).
You have a opportunity to see the wildlife from a horseback as you can rent a horse or go on a tour, at Fortunens ponycenter located in the southwest corner of the forest. The special thing here is that the deer don’t get scared away by the horses even with riders mounted.
As a beginner you can get guided tour ridings in groups in the weekdays starting at whole hours from 14 to 17 a clock and at sat, sun, holydays and school holydays at 10.30, 12.00, 13.30, 15.00, 16.30.
For experienced riders there are two hours tours on sat and Sundays starting at 9.30.
As individual persons you just have to show up at the times mentioned above if you are a group of 6 or more you are able to book a time Phone +45 45876058.
The price pr. Hour is 160 DDK. They have a webpage but its only in Danish.
Ved Fortunen 33
tlf.45 87 60 58
This is an area right by Klampenborg st. (a 15/20 min. train ride from down town) which is mainly just a large forest with great open plains. A perfect place to have a picnic, and spot some of the many different types of deers that roam freely about. In fact, if you are a true dane living in the area, you must have a picnic here every year. There are horsecarriages for the romantics, and in a corner of the area, there is an amusement park called Bakken which you can also stop by.(See my review of Bakken)