Hi,
I am a US citizen and I bought a house in Canada. Since I have an immigration application in process, I asked the immigration officer at the place where I cross (and will ultimately land) about this well before I did it. I have been very careful to do nothing to jeopardize my application.
Anyway, for the purposes of owning a house, I am a "seasonal resident" of New Brunswick. This is a category that works for people who own camps and cottages. Mine just happens to be a year-round house. I travel to NB on most weekends and during my vacations. I do NOT work in Canada; I don't even volunteer any more as I was told that it could jeopardize my application. I also don't overstay my official welcome (easy because I am employed full time in the US) and I never take things across the border in either direction without very carefully declaring them.
After I purchased the house, the next time I crossed into NB I formally stopped at the border crossing to "take possession" and to bring my goods into the country. The people at the border were very welcoming and positive and helpful. Of course, I had everything in my truck labeled and the forms all filled out and all of the documents about the house were in careful order, so I am sure that helped. But it was a good process.
I officially and permanently and regularly live in the US and I work in the US. I just happen to live in a border state so getting the seasonal residence was sensible for me. I don't know if this information will be useful to the OP.
Leslie Ann