This sounds like winter burn on your Dwarf Alberta spruce. I suspect that it's on the south or southwest side of the tree. During winter when the ground is frozen, the tree can't readily pull moisture out of the ground. Yet, on warm days it is transpiring and losing water. So essentially the plant is under mid-winter drought stress. It helps to make certain the soil is saturated going into winter. And if the tree is exposed, you may need to put up a temporary shade barrier of burlap or similar material to keep the browning from recurring.