OED lists both pronunciations for BE and AE (long versions first); M-W lists both (long version first); neither dictionary provides a “regional” tag. I’m familiar with the short version in BE; I may conceivably use, or have used, it sometimes; it’s not my default.

OT - I would avoid designating door, floor, as "long o [o:]:. The following R colors the vowel, and muddles the comparison with the other words in the list.

Here, for purposes of discussion (and hopefully clarification) is a four-way distinction of American English back rounded vowels, unmuddled by a following R:

Stewed: closed long U /stu:d/

Stood: open short U: /stʊd/

Stowed: closed long O /sto:d/

And, for completeness, though not a word, *Stawed: open short O /stɔd/

I agree with FehlerTeufel's suggestion - let's hear an example or two that we can judge.

PS - here's another minimal quad, in the same order: Cooed / could / code / cawed

In looking for examples of 'roof' /rʊf/, I came across a couple of discussions that also mentioned 'root' /rʊt/, so I suspect all those words may be in the same group with 'room' /rʊm/, at least for AE.

But I'm not sure about the theory that it might be characteristic of the US Midwest -- some participants in this thread seemed to suggest the opposite, if I followed the symbols correctly (U is evidently used to represent /ʊ/).

https://www.waywordradio.org/discussion/topic...

Using those other words, I came to some discussions about variation within both the US and the UK, with links to other sources.

http://dialectblog.com/2012/06/27/goose-room-... cites

the Harvard Dialect Survey

http://www4.uwm.edu/FLL/linguistics/dialect/s...

and John Wells citing Daniel Jones's EPD

http://phonetic-blog.blogspot.com/2010/09/roo...

One contributor mentioned a Wiki page on "Shortening of /uː/ to /ʊ/," which might be this one:

https://en.wikipedia.org/wiki/Phonological_hi...

In searching for it I also came across, e.g.,

https://english.stackexchange.com/questions/3...

https://www.antimoon.com/forum/t6657.htm includes this post:

As luck would have it, this US dialect survey had a question on words like that: http://cfprod01.imt.uwm.edu/Dept/FLL/linguist... . And you can look here: http://cfprod01.imt.uwm.edu/Dept/FLL/linguist... to see the percentages by state.

I haven't chased down all those secondary links, but my preliminary impression is that it does vary, but not always or only according to geographic region, and there's evidently also some room for disagreement over which pronunciation was 'older.'

In the late 50s and early 60s, my very English nanny used to say room with a short vowel. I’ve always thought of this as rather posh.

An interesting side note: We always used to say Goofy (Disney’s cartoon character) with a long vowel, but our art teacher – for some unexplained reason – had the nickname Goofy with a short vowel.

The online dictionaries provide audio files for both pronunciations, Macmillan dividing them between BE and AE, which is simply wrong; AHD gives only (what sounds to me like) a shortish pronunciation.

M-W (both, AE): https://www.merriam-webster.com/dictionary/room 

OED (both, BE, AE), for those w/ access.

Macmillan (BE, only the short/shortish, AE long): https://www.macmillandictionary.com/pronuncia... ; https://www.macmillandictionary.com/pronuncia...

Oxford (both, BE, AE): https://www.oxfordlearnersdictionaries.com/de... .

Collins (both, BE): https://www.collinsdictionary.com/dictionary/... .

AHD (AE, only a shortish pronunciation): https://www.ahdictionary.com/word/search.html...

FWIW some comments: (based on Longman Pronunciation Dictionary 1955 [LPD])

#6 Martin-cal:

Stewed: stu:d is AE; BR would be stju:d

Stood: stʊd OK for AE and BE

Stowed: sto:d neither AE nor BR:  AE stoʊd; BE stəʊd

door, floor: BE (in today's RP) has no r at the end of a word which could muddle the pronunciation: dɔ:, flɔ:. AE has both: dɔ:r, do:r, flɔ:r, flo:r

# room:

I am quoting LPD in full:

"ru:m, rʊm BrE poll panel preference: ru:m 82%, rʊm 19%. Some who say ru:m for this word on its own nevertheless say rʊm in compounds: see bedroom."

#5 hm-us:

for poof LPD gives pʊf (preferred) or pu:f (alternative) for both BE and AE.

#7 hm-us:

Indeed, LPD gives ru:f and rʊf (BE and AE) and ru:t and rʊt (although rʊt is not classified as RP in BR)

All this of course does not take into account any regional or dialectal variations.

An earlier query: related discussion: roof, room - Aussprache

(see esp. #7 for an AE native speaker who uses the shorter vowel sound)