Deer at Tidö Slott
Like many castles in Sweden, there is a fenced of area where the deers are wandering around on the castle property. The area is fenced off, but I think you can get through the gates to hike here. There are some limitations though, like not disturbing the deer and not accisible during some times of the year when the deer have young (or something like that). As I was on a trip to Västerås I didn't make a hike here, but I did take the time to walk to the back of the castle to look into the gardens. And yes, I was lucky enough to spot this group of deer not that far from the castle.

Outside the place.
Old wooden houses in the open air museum
Around Lake Mälaren
Västerås