TU B'SHEVAT, the New Year for Trees, began last night at sundown.
This year Adin Even-Israel Steinsaltz has an article on The Evolution Of Tu b’Shvat for The Jewish Week.
Also inspired indirectly by today's holiday, Elon Gilad asks Did ancient Jews worship trees? in Haaretz, with the sub-heading "The Hebrew words for 'oak' and 'terebinth' seem to derive from the ancient word for 'god - el."
Regarding the latter, I would not make too much of an apparent similarity between these tree names and the word for "god" in Canaanite; this could just be a coincidence. But it would not surprise me if ancient Israelites practiced divination by dendrology. Various forms of divination have existed in Israelite and Jewish circles from antiquity to the present and the practitioners did not and do not think of this as worship of anyone other than God.
But one ancient Israelite custom which was pretty close to tree worship and is only hinted at in this article, is the worship of the Canaanite goddess Asherah (see here and here) as consort to the God of Israel. The Deuteronomistic Historian complained about this (e.g., 1 Kings 16:33; 2 Kings 21:7, 23:14-15) and there is epigraphic evidence for it as well. It appears to have been a fairly widespread practice in some circles, and her symbol seems to have been a sacred pole or tree used in her cult. But this would not have been tree worship; rather the tree or pole would have been considered a receptacle for the essence of the goddess and it would have been she who was being worshipped.
But none of this has anything directly to do with Tu B'Shevat; it only arises because trees are also involved.