Antonovka is probably the only widely used rootstock for your conditions. Unless there is a local hardy crabapple alternative.

On second thought, I did the conversion wrong in my head. That is much colder than I was thinking. I'm not sure any apples can survive there without going to great lengths to shelter them. Do you know anyone that grows apples in your area?

72 degrees below zero? Good luck.

Here are a few rootstocks to look into:

Here is a link that might be useful: DNR Alaska apple rootstocks

how about a potted tree, one you can move to cold storage in winter?

If you regularly see -50C, you are probably in zone 1a, instead of 2a.

There is a note in Michael Phillip's book which mentions that crosses of siberian crab with Ranetka rootstock (itself hardy to zone 3) are often hardy to -50F (the lower limit of zone 2a).

Where about are you located,..I've been up in Fort McMurray, think it's 2a and seen lots of ornamental crab apples.
I would see if anybody in your area has anthything alike, then plant some and top graft some branches a couple of years later higher up,..you have better protection this way.

It's the top grafted apple you have to be most concerned of, less hardy then most root stocks.

I am in Athabasca, Alberta - some of the lower valleys get really cold in winter. I am at least a zone 2a or possibly a 1b (some 2a plants never survive the winter - not sure if they were correctly rated).

There are several apples on the farm that are over 50 years old and do just fine - but I have no way to figure out which rootstock they have. Everything I read seems to suggest that I need a rootstock for various reasons.

I just don't want to get an apple have it for 10 years just for it to die in a really cold winter - the last time we hit -58C many fruit trees rated 2a didn't make the winter. We have about a dozen trees that survived on the farm - but I have no idea what rootstock they have. They stop at 15 feet tall so I am sure they must have a rootstock.

I plan to take the top grafts from apples that I know can survive (besides, I really like those ones).

I am beginning to wonder if I should just skip the rootstock and see if I can't just get a branch to root somehow.

"They stop at 15 feet tall so I am sure they must have a rootstock. " - silversinger

I think 15' is probably a full size tree for your location. Trees are smaller when grown in locations that have very short growing seasons. It might be on its own roots if you don't see any evidence of a graft union. It would be a hardier tree without a graft. Do the roots sucker?

You could try rooting compound on new growth cuttings. If the tree suckers, you could also try getting them to root while still attached to the tree with a potting variation of stooling. If they are all the same variety and semi/self-fertile, you could try growing from seed. It doesn't sound like there are a lot of pollenizers to worry about in your area. Even so, some varieties will produce trees from seed that are true to the tree it came from. There is variety where live that has propagated itself along the countryside by natural seed dispersal. This is not typical of most apple varieties. It could be that self-fertility is one important factor in producing seedlings that are near clones of the parent. I'm not sure. Unfortunately, starts from seeds will probably take a decade before knowing if it was a hit or a miss.

I don't see any evidence of a graft, but it is over 40 years old and the trunk is 18" in diameter.
It doesn't come back true to seed - someone tried and they ended up with an ornamental crab.
I have never seen any of our trees sucker (if you are referring to suckering like the aspen and poplar do).

The link Swampsnaggs gave was very helpful, I will see if the greenhouses offer some of the rootstocks mentioned there.

Any advice on getting a cutting to root? I have one sitting in a damp peat/black soil mixture after I applied a growth hormone to the cut. Could be the wrong time of year to try. Our fall is rapidly approaching, and the last 3 nights have seen frost in low and open areas.

I wouldn't worry then about rootsock, ...just take your own apple seeds and grow from them,..got a orchard growing from seedlings, never had problems with rootstock.

Rooting them can be very challenging, ..most likely it will not work. If it does, have a feeling it wouldn't perform as good then, grafting to vigor roots, ..in harsh and short growing season you need something fast and vigorous, [trees still small] don't go with dwarfing stock.

Though I have no experience whatsoever growing in those conditions, I have tried rooting cuttings using rooting hormone/peat etc. I've also grown many seedlings. My gut instinct leads me to agreement with konrad. Grow out some seeds.