You can, for example, take a walk in Nordskoven near De Små Fisk or in Hvinningdal Skov, where there are several fenced dog forests, or you can choose one of the unfenced dog forests in the surrounding area of Silkeborg.
In Silkeborg and the surrounding area you'll find more than 10 dog-friendl parks.
Here is an overview of dog forests in Silkeborg.