You did not bother to tell us the model year of your Outback, but there is a known issue on some Subarus of the early 2000’s vintages with this symptom. The cause is clamps on the fuel lines that loosen slightly in very low temperatures. The dealerships are familiar with this issue, and there may actually be a recall for your vehicle as a result of this issue. Check with the dealership regarding replacement of the problem clamps.