I had the exact same setup but in a warmer climate. (in the South) An air conditioner is going to cost a lot of money to run, for a closet grow probably not too cost effective unless you have the money and don't care.
What I did was buy one of these sets
http://www.ebay.com/itm/Hole-Saw-Drill-Bit-Kit-16pc-w-Mandrels-Saws-w-Case-Wood-Plastic-Sheet-Metal-/171530890693
and cut 6 inch hole in the ceiling. I then connected my carbon scrubber and fan directly together and raised it so it was near the hole in the ceiling, (I had a shelf that was up high) then add a small amount of duct (home depot) to the inline fan and up into the attic. I then cut a 4 inch hole using the hole saw blade in the lower part of the door. That hole let fresh air in and the carbon scrubber/fan combo ran the hot and now smell free air up into the attic. If you're worried about cutting the door, you can buy a cheap one at home depot for about $20.00. Patching the hole in the ceiling (which will be a clean circle, you can reuse the sheet rock circle you cut) and buying a cheap door is far cheaper buying an AC unit and the power that it will consume.
My closet would get into high 90's or low 100's without those modifications but I was able to keep it about 5-7 degrees higher than room temperature with the simple ventilation setup.
I have a cool tube now and have tested just running the hot air through another hole in the door and it worked fine. So really you can get away with just two holes in a cheap door if you have a cool tube. One hole by itself for intake, one hole to exhaust the cool tube.
If you're concerned about stealth just make sure the fan is quite or muffled and run it into the attic then for the door intake hole staple/somehow attach a big tote tub, boxes etc to the door so it looks like it's sitting on the floor in front of the door. Cut a corresponding 4 inch hole in the tote tub/box and if needed add a little duct to connect it so air can be pulled in. I just kept a bunch of boxes and crap in front of the door but left space to make sure the fresh air intake hole wasn't obstructed.