I rode Dempster on Cannondate T1000 with 700x44 in rear and 700x35 in front. I rode Dalton and Russia on Trek 520 with 700x35.
My opinion is 700x38C should be fine for the Dempster. As Big Lew mentions, the wild card is getting wet rain turning things into sticky mud. I had some of that approaching Fort McPherson and that part of road was particularly soft then - but not sure tire width makes a huge difference for that condition.