What part of speech is long playing the part of in the bold parts of the quotations below?

• For one thing, it shows at a glance how much money is on hand for any particular purpose all month long.
• The fishermen stayed in their nets the whole night long.
• Some people prefer to live in places that have the same weather or climate all year long.
• He had told them to sit on the edge of the sandbox all recess long and not move a finger.
• Wild animals, driven by hunger, came all winter long to live close to the feeding station.
• Other friends worked hard all semester long and didn't feel any pressure at all as the final exam approached.
• One half of the labor actually expended in the cultivation of these grapes would have kept them in tip-top order the whole season long if they had been planted in four rows as already suggested rather than in twenty short ones.
• It suddenly came to him that he would never, his whole life long, see Gramps again.
• He did such good work, and so much, that nobody would question him. Plus he could go all shift long, and most of them couldn't.
• She realized suddenly how old and hurt he was, an elder with gray hair and loose skin, and yet he had been working with his paddle nearly the whole day long.
• All year long, all decade long, all century long, the sun just keeps on shining.

To me it looks like it’s acting as some sort of “adverbial postposition of time”, just as during is an adverbial preposition of time in phrases like during the night.

The problem is that long follows its NP complement, just as ago does in three years ago, making it more of a postposition like ago than a preposition like during. I think.

How should this sort of construction best be classified? The OED calls long an adverb here.

Edit

My confusion may be that I’m unclear about the transition from something being a modifier that takes a complement and it becoming an actual preposition/postposition/adposition.

I am not referring to long used as an adverb in such collocations as “How long have you been here?” or “as long as you like”. Rather, I mean what the OED gives as its sense 6 of long¹adv. the following:

6. Subjoined to expressions designating a period of time, with the sense: Throughout the length of (the period specified). [Compare German sein leben lang.]

It’s been used this way at least since Middle English; the first citation given is for “all year long” from back around 1290 ᴀᴅ in the South English Legendary (a source that provides 2359 quotations):

• c1290      S. Eng. Leg. I. 264/122
  Heore ȝat was swiþe faste i-mad: þoruȝ al þe ȝere longue.

This is not one of the entries that has yet been updated for the OED3, so perhaps the analysis has changed since the OED2. However, it is similar to the entry for ago adj. and adv, which has indeed been updated for the OED3, and which remains an adverb when used in phrases like “long ago” and “longer ago”, but which it classifies as an adjective when used in the more customary collocation of time, as with this recent citation:

• 2009     S. Craven Ruthless Awakening 32
  We agreed on the guest lists ages ago.

There appears to be some dispute about whether things like ago constitute actual instances of “postpositions” in English, or whether they are better left in their traditional categories of adjectival or adverbial modifiers that just happen to follow their modificand.

I am confortable with saying that nouns like home or Tuesday can be used adverbially, as in “I’m going home” or “I’ll see you Tuesday”, but this doesn’t quite seem like one of those to me. On the other hand, it does remind me of:

• I stayed through the whole night.
• I stayed the whole night through.

If the first is to be called a preposition, but the second is not to be called a postposition, then we have to call through an adjective “modifying” night and the entire thing somehow a noun phrase being used adverbially. That seems to be the very sort of classificational contortion as is being attempted with calling long an adjective, and I find both to be particularly unsatisfying approaches.

SUMMARY

A clearer explanation of what long is and is not in the type of collocations presented in the initial example list would be much appreciated. It’s ok if multiple models of analysis are presented.

PS: I do not have personal access to the recent work by Dennis Kurzon about adpositions in:

Adpositions: Pragmatic, Semantic and Syntactic Perspectives, ed. by Dennis Kurzon and Silvia Adler. John Benjamins, 2008

The Old English word lang has suffix forms -ling and -long, (“with the direction, duration, or length”), similar to -lic (“with the body or form”) that survives as the very common -ly adverbial suffix form.

The -ling form, once used in words like hinderling (“in the backward direction”) has been supplanted by another usage, the nominal diminutive: darling, yearling. The -long form still survives, with all three senses, in words like headlong, nightlong, and footlong.

The suffix is adverbial in directional modifiers like headlong and arselong, adjectival in metric modifiers like footlong and nightlong. When combined with a quantifier to form an adjectival or adverbial phrase, the metrics compounds break into their component words:

• I ate a footlong sandwich. [adjective]
• This sandwich is one foot long. [adjectival phrase]
• This sandwich measures one foot long. [adverbial phrase]
• We attended a nightlong party. [adjective]
• We stayed at the party the whole night long. [adverbial phrase]

As these express spatial and temporal dimension rather than relationship, it's not clear whether these are adpositions or simply adjectives with an idiomatic phrase order. However, the close similarity to a hole one foot through or party the whole night through suggests that they may indeed be postpositions.

@tchrist: Yes you are right, in all the above examples Long has been used as adverb, but as an adverb it's used as following

Adverb 1. for a long time

• How long have you been waiting ?

Adverb 2. a long time before or after a particular time or event

• He retired long before the war.

Adverb 3. used after a noun to emphasize that something happens for the whole of a particular period of time

• We had to wait all day long.

• They stayed up the whole night long.

(information courtesy OALD)

Long in all day long is like old in 3 years old.

All of your examples fit Merriam-Webster's definition 3b of long as "having a specified duration:"

• all month
• the whole night
• all recess
• all winter
• all semester
• the whole season
• his whole life
• all shift
• nearly the whole day
• all year, all decade, all century

In this usage, M-W simply identifies its part of speech as an adjective.