As well as the formal gardens around the House, Burghley is surrounded by a large estate landscaped by Lancelot (Capability) Brown in the C18th with parkland, avenues of trees and a lake.
There is free entry to this daily from 8am – 6pm (or dusk if earlier), after the the 6th Marquess instructed in his will that the Parkland will always be available free of charge for the benefit of the local community.
There is a “network”:http://www.gps-routes.co.uk/routes/home.nsf/openmap?openform&route=burghley-house-walking-route of paved road as well as footpaths. It is popular with walkers (especially those with a dog) and families.
There is a golf course which is the oldest in Lincolnshire and cricket pitch. The parkland is used for events during the year, including the Game and Country Fair and the “Burghley Horse Trials”:https://burghley-horse.co.uk/information/maps and access to the parkland is restricted while these are on.
I have written separate reviews for the Sculpture garden and the Garden of Surprises. These are entered by a gate to the east of the estate buildings and entry is included in the house ticket