Uath is the most awkward letter in the row, and its awkwardness is a useful thing to see, because the tree scheme has to work hardest here.
The name
Uath means horror, terror, fear. It is not a plant of any kind. This is not a contested reading; it is what the word means.
The sound
The letter's value is also a problem. It stands for h, a sound that Old Irish did not have as an independent phoneme in the positions where an alphabet would need it. Some scholars have argued the letter never had a stable value in ordinary use at all, and it is vanishingly rare in the stone inscriptions.
So the first letter of the second aicme is a character named after an abstract emotion, representing a sound the language barely used.
The kennings
The briatharogaim gloss it with phrases about an assembly of packs of hounds and about blanching faces, fear, in other words. The kennings agree with the name. They say nothing about a tree.
The hawthorn
The hawthorn appears in the later scholiast layer, and the reasoning behind it is visible: hawthorn is the fairy tree, dangerous to cut, associated in Irish tradition with places one should not disturb. If a letter meaning terror must be assigned a tree, hawthorn is the obvious candidate.
It is a good inference. It is still an inference, made centuries after the letter was in use, by someone applying a scheme.
Reading it now
The modern divinatory meaning (caution, the threshold, what should not be approached carelessly, protection through fear), is unusually well grounded, because it derives from the letter name rather than from the tree. This is one place where the folklore and the philology point the same way.
It just does not point at a hawthorn.