Question from Kay - Penshurst Place parks hunting lodge

Do you know how likely it would be that Penshurst Place would have a hunting lodge or some other kind of summer house in its parks around 1600? I've been looking into it, but so far I haven't found a lot about what was in the parks surrounding the estate itself during that time (as opposed to what's in the estate now), or what such buildngs would look like. Thanks for any help you can give me!