Why don’t they just live in Arizona for just under six months in winter and live in Canada for just over six months in summer like everyone else? 
Technically, there are generally no problems as regards the purchase, as long as the paperwork involved in the purchase is done correctly in Canada. I’ve supervised the signings of a few Arizona (and other state) land purchases, and there have been no problems–typically, I (as a lawyer) attest via documentation that I am qualified to give legal advice in the matter, and to supervise the signing; and I make sure that I have the necessary IDs of the Canadian purchasers, and everything is signed in the right place, and sealed by me where necessary. Note that it is always helpful if the American lawyer includes an instruction page and “sign here” tags, since the paperwork will always differ from that which I’m used to. But if things are clear enough, and I can understand the paperwork, it presents no problems and the conveyance is made as all parties intend.
I won’t comment on the immigration/health care questions. But as far as the land purchase goes, it’s usually no problem.
Thank you, Spoons.
This is the standard snowbird practice.
Keep in mind, you have that minimum stay in Ontario (or whereever) to remain qualified for OHIP medical.
If you stay more than 180 days in the USA (IIRC) out of 3 years, then you must file a US tax return - although unless they have weird incomes and are fabulously wealthy, they probably won’t pay any extra taxes over what they already pay in Canada.
If you overstay that 180-days a year tourist limit, you risk the border Nazis coming and tossing you out and you won’t get back in again. Always leave a little leeway for emergencies or sudden return visits (i.e. house problems down south). TO be fair, the Mounties have been known to chase AMericans who overstay their 180-day limit too.
I knew a woman who had a minor heart problem (hospitalized for a few days) at age 60, she had to skip doing the USA-in-Winter thing for 3 years, because she could not afford the travel insurance. If she was healthy for 3 years, the travel insurance cost would drop to affordable levels.
Usually travel health insurance will fly you back to Canada if it’s serious, because an airlift to Canada is cheaper than a week in a US hospital. I know of one senoir who was found lying in his bed in Arizona partially paralyzed from a stroke; his friend loaded him in the SUV and drove him non-stop back to Canada because the fool did not have health insurance.
My grandparents generally rent a condo for three months in the Winter in South Carolina, and spend the other nine in Ontario, plus smaller travels throughout the US periodically. They used to own a place in Florida, but it all got too much for them and they wanted something easier to maintain.
Grandma had a very easy course (thank og) of breast cancer and they also weren’t able to travel to the US for an extended period of time due to the insurance costs. Now that she has reached 5 yrs+, insurance isn’t an issue. Grandma had her hip done last August and they were able to go to SC this past Winter, that procedure really had no bearing on her insurability, AFAIK.
They do have to make sure they are in Ontario for the required time periods to qualify for their health care. They are also very cognizant of the insurance coverage dates and make sure to add a buffer zone, just in case.
My father has tried to talk them into retiring full-time to the US to be near him. They refuse to do it.
Seniors in the US are covered by (U.S.) Medicare. A Canadian immigrant in this situation may not be eligible for it.
This is one big reason why my elderly aunt, who lives in Montreal, will probably never be able to move close to her son, who lives in New York, even though it would otherwise be a good idea.
I think Hari Seldon has commented that he’s in the same boat - in medicare exile in Canada, because he didn’t pay into US social security while working in Canada.
Is it really likely to take that long? I got my green card through marriage two years ago and it was four months from start to finish, and the parents would be the same category. Or does it make a big difference if you do it either in or out of the country?
Yes, it does make a big difference. I have a client who is in Canada, and whose immigrant petition (I-130) was filed in early January, and she ain’t done yet. Given, some of that delay was on her end getting documents and other info to us, but if you’re filing from abroad, it’s a multi-step process: first you file the I-130 with the Service Center, and then after that is approved, USCIS sends the file to the State Department, which then sends out a request for forms and biographic documents, which are filed with the National Visa Center, which then reviews everythinkg, and if it’s complete, they send the file to the appropriate consulate, which schedules and interview.
If you are filing in the U.S., and the visa category doesn’t have a quota backlog as in your case, you file everything at the same time with USCIS, so you get a much more streamlined process.