I wouldn't call it an adjective, I'd call it a modifier. A modifier is:
a word or phrase that adds to the meaning of another word or phrase by giving more information about it
A Wikipedia article about modifiers explains that modifiers can be adjectives, prepositional phrases, or other nouns. For example, consider this sentence:
Some loud birds are chirping in the oak tree with the dead branch.
In that sentence:
- loud is an adjective modifying the plural noun birds,
- oak is a noun adjunct modifying the word tree, and
- with the dead branch is a prepositional phrase acting as a post-modifier to the noun phrase oak tree.
The word oak is functioning a lot like an adjective – I mean, oak tree looks a lot like yellow car – but I don't think it's entirely correct to call it an adjective.
When parsing a sentence, it can be hard to tell the difference between a noun phrase (like oak tree) and an adjective-noun pair (like hot soup). We can check a dictionary to see if the word in question gets listed as an adjective in the dictionary. For example, a word like compound will have definitions listed a noun and as an adjective, because the word can be used either way. However, most of the dictionaries I checked only listed oak as a noun, so I'd be more inclined to view it as a noun phrase. That said, I wouldn't want to be too dogmatic about the matter.