Yes, Møn is known as the best riding country in the nation due to the rolling hills and forests. Having not tried all areas myself, I don't know, but I do know that I'd love to ride here for precisely those reasons as there are forest trails everywhere and the hills glow in the evening sunset and would make a great up and down trek. You can go for a trek with the Møns Klint stables next to the youth hostel. They have all sorts of horses and some are suitable for beginners too. Prices vary according to how long you go for.
There is also an Icelandic horse centre (second link) - Icelandics are popular trekking horses in Scandinavia and very sure footed.
There is a strong hunts tradition here too so you might want to contact the stables if you want to join their annual events.
Updated Oct 1, 2007
Address: Langebjergvej 1, Borre
Website: http://www.klintholm.dk/docs/ridepens.htm
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Reviews and photos of Møn attractions posted by real travelers and locals. The best tips for Møn sightseeing.

Yes, Møn is known as the best riding country in the nation due to the rolling hills and forests. Having not tried all areas myself, I don't know, but I do know...
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