What are you interested in photographing while you're up here, and what's your (and to a certain extent, your gear's) tolerance for cold?
The best time to avoid mosquitos is October through April. It's also the best time to see the northern lights. We'll have snow cover by October 31st. Freezing temps usually start by the 2nd week of October. Sometimes the bottom drops out: I've seen -62*F by early November. The last couple winters it's usually stayed around 0 to -10*F for highs, but this past winter was colder. It was -58*F when I came back from vacation in mid January and stayed cold (-20 to -40) till almost the end of March it seemed like. Typically the snow melts by the last week of April, and then the bugs thaw, the night goes away for a couple months, and before you know it it's summer! Unless it snows, like it did on Memorial Day this year, but it melts pretty quickly.
"Spring" in the north seems to be happening about now-ish in interior Alaska. We're fully past bud break on the trees and should start to see wild flowers blooming any day now. It hasn't gotten dark out since about the last week of April and won't be again until the last week of August or so. June, July, and August are wonderful times to be in the North. The light in the "evening" is truly magical. Sitting outside under the midnight sun is part of why we put up with the winters. It might rain, but the sun's always out when it stops. A bigger concern is wild fires as they can make it pretty smoky and miserable.