After updating the horror award and nominees list on the sidebar (it should now be current up to the most recent Bram Stoker nominations), I wondered which currently operating magazines published the most award winning horror fiction, given that print periodicals were in decline. I looked publication information for all award winners nominees from 2007 onward, and counted the number of award winners nominations. In addition, since 2009, the British Fantasy Award has a category for "Magazine".

The results fall into three categories: currently in print, currently online only, and defunct (including magazines like Postscripts, which are now published as individual anthologies, not as subscription periodicals).

Most Award Winning Horror Fiction, Print Periodicals:

• The Magazine of Fantasy and Science Fiction has had 21 different stories nominated since 2007. It is far and away the most frequent venue for publication of award winning horror.
• Black Static comes in second, having 9 publications nominated for awards. 8 of these were for the British Fantasy Award, which has also nominated Black Static for Best Magazine every year since it started giving that award (6 times). A TTA publication.
• Interzone is also a TTA publication, and comes has been nominated for the BFA Magazine Award 5 times, but no specific stories have been nominated for awards.
• Asimov's Science Fiction has published 3 pieces nominated for horror/fantasy awards.
• Cemetery Dance has surprisingly only had 2 stories nominated since 2007: "The Inner City" by Karen Heuler, and "The Crying Child" by Bruce McAllister. They have been nominated for the BFA magazine award twice. This amazed (and somewhat disappointed) me since I had a subscription to Cemetery Dance when I was a kid, and at the time it seemed to be full of amazing horror.
• One story nominated: Dark Discoveries (despite having consistently talented writers) has only one nomination, as does Weird Tales. Crimewave, the third TTA Publications title, has one nominated story. I'm not actually sure if Dark Moon Digest published a nominated story or not: Joe McKinney's story "The King of Marvin's Gardens" (Bram Stoker Award Nominee) was published in a Dark Moon anthology called "The Best of Dark Moon Digest", but I can't find evidence that it was ever published in Dark Moon Digest magazine.

Most Award Winning Online or Electronic Publications A few of these publications also have a print magazine available. I'll note that parenthetically:

• Subterranean published 10 nominated stories since 2007. They used to be a print publication, but are currently online/electronic only.
• Clarkesworld has published 7 different award nominated pieces, and was nominated for the BFA Magazine award once.
• Tor.com has published 6 award nominated pieces (all but 1 were nominated for the World Fantasy Award).
• Lightspeed has published 3.
• Beneath Ceaseless Skies has published 2.
• Strange Horizons has published 2, and was nominated for the BFA Magazine Award once.
• Single nominations: Lovecraft eZine (also a print publication), Daily Science Fiction, Horror Drive-In, Nightmare Magazine, Fantasy Magazine, Electric Velocipede (no longer active?), Estronomicon, Apex Magazine, The Horror Zine (no story nominated, but BFA Magazine award nominated once), Theaker's Quarterly Fiction (again, no individual stories but was nominated for the BFA Magazine award), Shroud Magazine (Not sure how to categorize this: you can't subscribe to it, but they do seem to publish on a regular schedule, and they seem to consider themselves a magazine rather than an anthology series).

Most Award Winning Publications that are not Periodicals

• Postscripts leads here, with 9 different award winners and 1 BFA nomination. Poscripts was originally a periodical magazine, but is now an anthology series, published irregularly.
• Shadows and Tall Trees, with 1 nominated story and 3 BFA Magazine nominations, is also a (yearly?) published anthology series now.
• The Uninvited, a digital magazine, still has a website but does not seem to have published anything since 2011, and has only 2 issues.
• Completely gone: Murky Depths (2 BFA Magazine noms), Chizine (2 story noms), New Genre (1 story nom), Doorways (1 story nom), Midnight Street (2 BFA Magazine noms).

Mainstream Publications

• Tin House: 3 different nominated stories, "A Murder of Crows" by Elizabeth Ziemska, "The Summer People" by Kelly Link and "Reeling for the Empire" by Karen Russell.
• New Yorker: 3 different nominated stories: "Home" by George Saunders, "The Dinner Party" by Joshua Ferris and "Procedure in Plain Air" by Jonathan Lethem
• One nomination each: Conjunctions (for Peter Straub's "The Ballad of Ballard and Sandrine", nominated for two different awards), Esquire (for Stephen King's "Morality"), The Paris Review (Ohh la la, for Aimee Bender's "Faces"), The Atlantic Magazine (Stephen King's "Herman Wouk Is Still Alive"), and, surprisingly, The Iowa Review (for "Max" by Jason Ockert).

edits: formatting, clarification