Just seems odd considering Spain and France weren't particularly maritime nations and yet they both had a lot of oversees holdings and it doesn't make sense to me why Denmark never had anything more than Iceland and Greenland (and a few negligable Islands across the world)
Denmark actually did have overseas holdings during from 1618, when the danish King Christian the IV sent a small expedition to Ceylon (todays Sri Lanka), until 1917 where the last remaining holdings (Danish west indies) were sold to the US for 25 million dollars. During this time Denmark also had som smaller holdings in Tranquebar, India and on the Gold Coast. Though the holdings in Africa and India were not really colonies, they functioned more like trading stations with several protestant missions attached.
Denmark's drive for holdings where just like all other european powers driven by mercantilism (from the french word mercantile), where an positive trading balance were wanted, which then would lead to a higher tax base. To obtain this the government at the time would increase import taxes and decrease export taxes, the problem with this system was that every country in europe would do the same.
However the colonies in Africa and India did not provide any real profit, and only the colonies in the Danish West Indies provided a profit, but only for a short periode of time. Which ultimately led to the sale in 1917.
Eventough Denmark did have a proud naval tradition at the time, it did not have the economic surplus to rival nations like France and Britain. This plus the factor that a great deal of Denmark's foreign policy at the time was specifically aimed at getting Skaane back from Sweeden, which removed some of the focus from the Caribbean, Africa and India.
I hope this answers your question. I have provided some sources, keep in mind they are in danish though.
In 1807 the British attacked Copenhagen in the aim of capturing/sinking the main Danish fleet, basically to stop Napoleon getting them in the future. This would have severely hampered any overseas expansion.