Would a falling tree not be considered as "an act of God" in Insurance terminology and not covered by insurance at all.
Not necessarily.
Act of God [Vis Major] can exist in two contexts.
1.
Insurance policy wordings.
It might appear in the wording of some insurance contracts.
That said, I have not seen it in any insurance contract / policy wording for years.
Almost certainly it does not appear in mainstream policies like public liability.
2.
Law.
Act of God has a meaning the essence of which is that some natural event of an unforeseeable and or unpreventable nature has happened and it could not by any amount of pains or care or foresight have been avoided.
Falling trees.
In relation to OP's specific question a claimant would have to establish negligence on the part of the owner of the tree.
This would usually require evidence of the state of the tree at the time that it fell.
The tree would need to be examined before it - the primary evidence - disappears.
A couple of photographs immediate post accident could help if there is discernible evidence of rot.
If the tree was defective liability should attach.
If the tree was free of defect it would then fall in to the Act of God territory for which no liability should attach.
I don't think people tend to plead Act of God much these days. A simple denial of negligence should cover the issue.
At a practical level OP's motor insurers should cover the loss of the vehicle - if comprehensive - and the insurers can consider subrogation rights against the tree owner.
Most importantly of all the OP actually survived to drive another day
