There are two factors that come to mind for me - one is that some non-hardy shrubs can experience a lot of dieback but return faithfully presumably forever. In my yard this include Euonymus alata and Purple-Leafed Sandcherry. I removed the latter because I was sick of it dying to the snowline every winter.

Woody trees might grow for several years but die in a particularly bad winter. There is a horse chestnut in my town just north of Winnipeg, and there are a couple I've heard of in Edmonton. But Edmontonians have better luck with tender plants than my area so I think they've earned the 1/2 a zone difference.

I like to push zones, but not particularly with trees...they're too expensive for something that might not work, and if they do work, well, I don't really want something else big in the yard! I do have an oak tree that I was given. It's all of 2 feet tall after, oh, maybe 10 years? Like northspruce's sandcherry, dies to the snowline. And last year, the person who gave it to me cut off the one branch that never dies because it was lopsided. It's getting quite a few new branches, but I have no hope for it long-term...someday, it's being tossed out!

I applaud you for trying, because there are those freak trees you see now and then that you look at and say "those aren't supposed to grow there!" So you could get lucky.

But having widespread success with trees that aren't hardy is very unlikely. Like Northspruce said, when you plant a tree that isn't hardy it may be fine for a few years, maybe 10, and then it is that much more of a crushing disappointment when it suddenly fails.

I try to content myself with the wide variety(though I often wish it was wider, ha ha!) of trees that we CAN reliably grow here.

I certainly don't expect that all the trees will survive -- I expect that the Gingko will sputter along for a few years before finally dying, and the Chestnut probably won't get very far, either -- but there probably will be a few outlier trees that will pull through, including both hackberries.

I'm going to continue my experiments, even with the expected negative results, as the accepted vegetation zones don't seem to take winter moisture levels into account -- just minimum temperatures. When I lived in Calgary, for instance, I had a lovely Butternut tree that grew very well in my sheltered back yard, but other "hardy" trees didn't do well at all with our frequent freeze-thaw cycles and very arid winter conditions. Peace River, on the other hand, has colder winter conditions, but we usually have a thick and stable snowpack with constantly low temperatures. We also get more consistently warm summer weather in the river valley. My guess is that any tree/shrub that can survive in central New Brunswick and the Saguenay has a good chance of making it here, and so I'll use that as my guideline.

I'll also like to add that I'd like to see a further calibration/refinement of the Canadian Hardiness Zone map for far northern areas. Yellowknife is classified as zone Oa, but this is probably inaccurate given that the city does get a mild moderating effect from Great Slave Lake. I saw quite a few "southern" trees when I lived in that city, such as Green Ash and the ubiquitous caragana, and they did quite well. There's also something to be said for 24 hour sunlight during the summer: many people produce bumper crops of corn in Ft. Vermilion, 300 km to the north, but it's definitely an iffy proposition for the rest of northern Alberta. It just seems ridculous to lump in treed and productive agricultural areas with tundra in zones 0 and 1 just because of shared low temperature values.

Well I think it's great that you are experimenting with pushing the zone limits. Even if there are failures it is the experiment that is the fun part. Heck, a few lost dollars on plants is nothing -- it's like a night out at the movies, only the movie is over in 2 hours, whereas your plant can go for years or longer.

I tried ginko here in Edmonton but wasn't successful. It died after its first winter. It actually leafed out in the spring, then died after a few weeks. I believe the roots were killed during the winter because we had little snow and its roots were very shallow being a newly planted tree, so there was enough water in the trunk to allow the leaves to come out, but no roots to supply new water and nutrients. That said, there is a ginko growing at the University of Alberta. I think it was planted as a sapling about 20 years year ago. I saw it about 10 years ago on a plant tour and haven't seen it since, but I see it is still listed on their plant tour for this year. And there is a very healthy ginko in Drumheller (zone 2b?) that is short (about 10 feet tall) and stocky (trunk about 6 inch diameter). Last time I was there (2009) I met the owner of the house and he was thrilled that I had been following this tree over at least the past 10 years. He claims it was planted in the 1960s and that he prunes it regularly to keep it a small tree. I'll attach a photo...
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I have a sugar maple growing in our backyard that I planted as a seed (collected in Barrie, Ont.) around 1992. It got about 10 or more feet tall, then we had a severe winter around 10 years ago and it was killed down to about 1-1.5 feet above the ground. But I left it alone, and it is now probably 15 feet high, with a multi-stemmed trunk, more like an upward spreading bush. I know of some better specimens in Edmonton about 30 feet tall.

I have a butternut that is about 15 ft. tall by 15 ft. spread, planted as a seed in the early 1990s. It seems healthy and has produced nuts for the past 5 years or so, but I know it isn't fully hardy because it gets a big vertical split in the trunk each winter.

I tried a Star Magnolia but never got it to bloom. It came back each spring for about 3 years, but a little smaller each year due to winter dieback, and I eventually took it out.

I've tried black locust (Ontario seed) but it winterkilled each year above snow-line so I removed it. I tried dwarf Catalpa (seed from Gardens North) said to be hardy to zone 4, but it also winterkilled above snow-lines so was removed after several years.

My six hybrid tea roses have been much more successful, winterkilling to the ground each year but re-growing quickly so they reach 3 feet or so in summer, with loads of blooms. Those have been in almost 10 years.

Then there's Edmonton's famous horse chestnut growing downtown, now something like 75 years old. There was a program a few years ago to distribute seedlings from this tree and get them planted around the city, but I don't know how successful that was.

George Pegg Botanic Gardens northwest of Edmonton has a nice black walnut tree that produces nuts.

And you may have come across the posts from that guy in zone 4 in Colorado(?) who grows palm trees outside, though he does use an elaborate heated-box system to protect them during winter.