One more data point:
Was watching a Hallmark movie recently. One of the characters was giving a brief “history of Halloween” tidbit. He pronounced Samhain as what sounded all the world to me like “SO-win” Read that as the English word “so” followed by the English word “win” in American “newscaster” English.
I don’t have any hard data to back this up, but my general impression is that in recent years there’s been greater awareness of the correct pronunciation of Samhain. When I encounter the word in pop culture, more people seem to be pronouncing it correctly–or at least, pronouncing the “mh” part as an English “w” sound.
For example, as silenus mentioned, Gene Simmons pronounced it “sow-in” in the Halloween episode of Jeopardy!. Sheldon pronounced it the same way on last week’s Big Bang Theory episode.
It’s my impression that awareness is spreading that Samhain is not pronounced according to the rules of English orthography, and that a greater number of people are taking more care to give it something closer to its correct pronunciation.
Maybe, maybe not. For example, the reason we have ph = f in English is because the word came from Greek and had the letter Φ (phi}. Philosophy = φιλοσοφία. In Spanish, it’s filosofía. So, it’s possible we would have invented some sort of marker in English to denote that the word came from Irish.
All things considered, these aren’t unreasonably awful Anglicized pronunciations of a Gaelic word. Just don’t say it’s the authentic Irish pronunciation, like the New Jersey folks who say that “gabbagool” is the “Italian” pronunciation of capicolla.
Maybe not Italian, but is it possible these folks are speaking Neapolitan?
Anyway, this is a good a time as any to remind everyone that not all Irish was always written with the Latin script; some of it was written in Ogham. 
I don’t know enough to comment on the exact relationship between Latin script and Ogham script, or how phonetic Ogham spelling was at the time.
I’ve asked around and have been told that these what I call “Northeastern US Italian restaurant” pronunciations aren’t part of any real language or dialect from Italy.
This article seems to suggest that they come from an amalgamation of features from various southern Italian dialects that mixed in New York and other North American cities –
It’s a lot more like Neapolitan/Sicilian dialect than it is like standard Italian or northern Italian dialects. Even your cite says some of these pronunciations are in part remnants of southern dialects. Short answer: Southern Italian dialect.
The article says that they are from real dialects in Italy, primarily southern dialects. They just aren’t spoken as much any more because Standard Italian, based on northern dialects, has largely supplanted them.
Those pronunciations were, and still are, prevalent in my neighborhood in the Bronx, which was largely populated by immigrants originally from Naples and vicinity.
I really don’t see how my description of the article was materially different from the two of yours.
I said 1. This is what I’ve heard personally when I asked. 2. This is what this article says. That’s two separate pieces of information. Are you confused because I didn’t insert a “but” bectween them?
You didn’t make what your point was at all clear. You appeared to be countering the speculation that the pronunciation was Neapolitan. It is, in fact, Neapolitan.
Probably, by now, “Neapolitan with a strong American accent” would describe most such pronunciations. Children of immigrants learn a lot of their accent from their non-immigrant friends.
A few more bits and piece:
Samhain is used also in Irish to denote the whole month of November. Mí na Samhna.
I could swear there is an old episode of Dr Who featuring an English witch that pronounced it “Sam Hain” too. I’m no Whovian, saw the episode probably 25 years ago but IIRC it featured a contemporary English setting circa 1970 and was in black and white.
My most treasured learning from my time taking bagpipe lessons was: how to spell/pronounce piobaireachd. (Pee-brock.) I’m just waiting for someone to ask.