Wiltshire Police said the incident happened at about 17:45 BST on Saturday on The Avenue.
Dorset and Wiltshire Fire and Rescue Authority says it wants to secure more council tax funding.
Wilton windmill, in Wiltshire, is more than 200 years old, and is the last working one in Wessex.
The circle, described by a photographer as "spectacular", has since been removed.
One-off additional government funding has been found to save the stations in Wiltshire.
Christopher Saunders-Pope, from Wilton, was jailed for child sex offences and drug possession.
A councillor said local firefighters were among the responders to the Novichok poisonings in 2018.
Dorset and Wiltshire Fire and Rescue Service says it needs to close stations to save money.
Campaigners pulled the stunt in Dorchester over proposals to close eight fire stations.
