"the 'first/last' of the [day/night/week, etc.]" for "the 'beginning/end' of the [day/night/week, etc.]
I think the sources you cite are mostly outliers and not the norm in North America. Novelists often experiment with form and language and are trying to find new ways to say things, which is what I think Stephen King did here. I do believe at the first of winter is sometimes used, because the phrase as a whole has some poetic beauty to it (compression of language, and a contrast between the precision of the word "first" and the vagueness of the changing of a season). All the other quotes seem unusual to me, including the Random House example. The Bible analysis seems like it's intentionally trying to sound archaic and flowery, perhaps to match its subject matter.
It's worth noting that there is a difference between at the first of day and at the first of the day. They're both uncommon, I think. The former implies a general notion of what a day is, and as such is more poetic -- similar to at the break of dawn or since the beginning of time or at the first of winter. The latter seems to refer to a particular point in time and appears to be used mostly in Western states.
It's also worth noting that the first of the month is common, but I've never heard at the first of the month. I believe Americans would say on the first of the month instead.
http://corpus.byu.edu/coca/ offers 12 examples of "the first of the day" and each one uses "first" as a referent to a previous noun.
"He smoked a cigarette, the first of the day."
There are no matches for "at the first of the day"
http://corpus.byu.edu/now/ gives tons of examples of "at the first of" and some refer to times. There are several from the midwest (Arkansas, Denver), but there's also one by an author born and raised in Tennessee and currently residing in Wisconsin: Alex Bledsoe.
" a relief to be away from London, after the zeppelin air raids at the first of the month. Here in Wales, no trace of the ghastly war could"
Who's to say whether he picked it up in the south or midwest.
On the whole, though, it appears to be a midwestern phenomenon.