Yes, because you're using this compound as a pre-head modifier, ie. before the noun (side), then it's probably best to hyphenate it.
But please don't call it an adjective! Neither "mountain" nor "facing" are adjectives, they're a noun and verb respectively, with the noun "mountain" being the head word. Thus, it's actually a noun phrase functioning as a modifier.
Hi, thank you and thank you for enhancing my understanding (and also reminding me of past lessons :)). Thanks again!
Hi David
I revisited the compound "mountain-facing" in your example and, on reflection, I think it would be better to call it a 'compound adjective'. Although the first component, "mountain", is a noun, the head is actually the second component "facing", which is a present participle. Present participles do have an adjective-like function, hence it better to call it an adjective.