i dont have a dog, but i am a in scouting and i know that a lot of scout sites let people on for the day just to go walking. all you have to do is say hi to the site warden so he knows that you are on site and how many of you there are for fire purposes.
my fave site is great tower, which is near bowness on windermere. it has amazing walks up to great tower rocks and there are quite a few routes so you cant really get bored