All the seed drop rates are less than one, and trees don't spread out or respawn. It is technically possible to run out of trees, but the effort required is the stuff of legends. It may be a hazard for 1000 or 2000+ days, but it's still possible to renew wood by hunting greydwarves.

It'd be nice to perhaps be able to purchase tree seeds from the trader, or offer another trader with special purchases.