Those are some sweet boot you have there Ron! I bet they come in nice and handy when walking the dogs in less than favorable weather!
Kiwi, I love that such a simple question drew so much conversation. I agree with a lot of what the others have said. I would generally expect people to remove their shoes when entering my house but if they didn't, it wouldn't bother me enough to say anything. Once in a while you can catch me walking around my house with my shoes on!
I do believe it has a lot to do with the fact that most of the year our shoes aren't clean enough to walk around the house in and we are conditioned to remove them even in good conditions.
I found that in NZ that the outdoors seemed to be more included in peoples living space. Doors were often left open, windows usually were open to help air the home out and the windows didn't have screens!! People seemed to walk in and out more frequently probably due to the fact that the yard was used more for living like laundry and eating outside. So wearing shoes all the time just seemed to make sense. At the same time a lot of my friends were just as happy to not wear any shoes at all! I was always shocked to see the guys running after sheep in the paddock with no shoes on!
I wouldn't be offended if you wore your coat inside, but you would get a few looks! You should bring some of that fantastic merino wool, that will keep you nice and cozy!