The shop in Fairbanks would be the closest... we're about 125 miles off the Arctic circle, and about 500 miles from the Arctic Ocean.
I've never heard them discuss a trip up north. They focus almost entirely on warm water diving, with trips to Valdez/Whittier as necessary for certification. Lots of local stuff when the water's thawed (April-Early October).
There's some major logistic hurdles to tackle. The drive up to Deadhorse / Prudhoe Bay is murder on vehicles. You literally bring 3 spare tires and hope you have enough to get you there. The oil companies aren't particularly thrilled with having people up there, and you might not be able to get out onto the ocean (you have to cross through their property), without being part of a tour group. Used to be that way anyway... bout 2 years ago, might not be the case anymore.
So... what if you fly into Barrow or Prudhoe? That'd be somewhat more convenient... but still rife with problems. No local dive shop up there (would only be open 3 months out of the year), so you'd have to bring all of your own tanks. The fire department -might- have a compressor. So either way, you've got to get that stuff up there. Alaska Airlines Air Cargo could ship a dozen tanks and a compressor up there for around $500 (about a buck a pound)... so, it's not horrible.
I've looked at the charts for the area, and it's shallow (<20 feet) until quite a ways off shore.
So.. with all that said. I've heard the diving can be very nice. My University has done a lot of research up there, here a link to an article:
http://www.uaf.edu/seagrant/NewsMedia/02ASJ/10.04.02boulder_patch.html
I'd love to dive the Arctic Ocean, but I don't have the energy or knowledge to plan a trip up there.
Did I mention the polar bears?