Compound Adjectives and -ed
This must not be taken as a definitive answer. Only hints too long to fit in a comment.
A - In order to form a compound adjective of the type adj+noun-ed, I'd say:
1- the noun should be able to transform into a reasonably comprehensible ed-adjective
- temper → tempered (s.o. or sth with a temper, seems OK)
- chair (n) → *chaired (doesn't seem to make sense)
2- the adjective in the first part of the compound word must fit with the noun-ed adjective.
- a blue-eyed boy seems OK
- a blue-tempered boy doesn't seem to make sense
B- I've just gone back to an academic paper I'd read a while ago exploring compound adjectives and in particular "the noun + -ed structure".
Here's a paragraph from this paper, it doesn't really answer the "why" in your question, but points toward a possible answer. (Paper's in French, translation mine).
Many linguists have pointed out that this type of compound adjectives (adj+noun-ed) is mostly used when describing a physical (blue-eyed) or mental (bad-tempered) characteristic. This physical characteristic doesn't only apply to people but can be found in animals (short-winged, red-tailed) or objects (red-roofed, sharp-pointed). Assuming that the adj+noun-ed compound adjective gives a definitory attribute to the noun, some linguists and grammarians will be inclined to refuse compound adjectives whose first word would express the point of view of the speaker.
Further on in this paper the author compares the compound noun "middle-age" to the adjective "middle-aged". Could we imagine short-temper as a possible noun? Then could we say the -ed suffix differentiates the noun from the adjective?
A question with/without “-ed” for the compound adjectives formed by “adj.+noun”? had been asked on english.se, and thanks to FumbleFingers for pointing out to John Lawler's comment on the disappearance of "ed" in spoken (and consequently written form) English.
Adjectives that precede nouns are called attributive adjectives e.g., an angry man. Adjectives ending in -ed or -ing are called participial adjectives because they have the same endings as verb participles. However, not all participial adjectives end with -ed (past participle) and -ing (present participle), if a compound adjective contains an irregular verb than it will take the past participle ending.
a hand-written letter
a candle-lit dinner
an easily-misunderstood question
a built-up area
Often a compound adjective is written with a hyphen, especially if it precedes the noun. Many participial adjectives have no corresponding verb, in which case they are formed by combining a noun with a participle:
alcohol-based chemicals
battle-hardened soldiers
a tree-lined avenue
a short-handed team
a short-tempered man
a kind-hearted girl
Compounds formed by a noun ending with -ed are hyphenated in any position in the sentence hence, the first example could be rewritten as "chemicals that are alcohol-based" likewise "a short-tempered man" and "a man who is short-tempered". But in the case of
a man with a short temper
in this phrase, there is no compound adjective, short is an attributive adjective qualifying the noun, temper. Consequently, many of the given examples can also be rewritten without using a compound adjective and a hyphen.
- a dinner lit by candle
- a question that is easily misunderstood
- a letter written by hand
- a girl with a kind heart
More information, for those interested, on compound adjectives see this page.
Thanks to @Edwin Ashworth for pointing out that hyphens are necessary to disambiguate meaning thus you can have 'a man-eating shark' but the phrase, 'a man eating shark' contains a completely different meaning.
"wooded mountains" The ending in "wooded" is not the normal ending of verbs as in "open/opened/opened". When -ed is added to a noun is becomes an adjective meaning having something or being provided with something. Some examples: wooded mountains - provided with wood, snow-capped mountains - provided with caps of snow
This type of word formation was already in use in Latin. Latin fortuna meaning luck, Latin fortunat-us meaning having luck, favoured by luck or the goddess of luck.
-The suffix -ed just makes a new adjective out of a periphrasis (preposition+adjective+noun), allowing you to make your sentences shorter and more elegant. So instead of saying a man with a kind heart you say a kind-hearted man.