What about the place of origin of the tree? I read somewhere that sometimes our nursery trees are grown in the US quite a bit south of here. When I was a kid we planted a red maple from Muskoka in our back yard and it always turned red and shed it's leaves early. Does the tree adapt completely or always retain some of it's inherited range of behaviour?
You are correct.
The tree's origin matters, so does the origin of its seed.
For naturalization projects it is typical to specify the climate zone of the seed.
The issue is at you point out, trees from different climate zones are adapted to those zones.
So your Red Maple had a shorter growing season, because the growing season is shorter in Muskoka.
Likewise, a Red Maple source from Kentucky will have a longer growing season.
However, it will also not be cold hardy, in part for that very reason. The tree will try to keep growing through lower light levels and colder temperatures into November, and when the cold hammers it, it will be in trouble.
It would likely die, but at the very least it would die-back, and shed multiple branches as it tried to conserve itself.
In respect of adaptation, no a tree can not adapt during its own lifetime.
It may adapt its seeds.
There is some discussion in the forest gene ecology community about all of this, in relation to climate change.
Some suggest that we might want to purchase trees/seeds from one climate zone south (but not futher) so that trees will be better adapted over the course of their lives.
One climate zone south is Lake Erie, North Shore.