Won't run smoothly in cold weather

I have a couple thoughts - first the EGR system may be restricted causing an issue for you. This is common on older higher mileage 5.0L V8s. The upper intake has to be removed to clean the passages in the intake. The valve may be sticking too. Secondly, the Idle air bypass valve may be sticking or causing a problem allowing air into the cold engine. There are other possible causes too, but I feel like you will be on the right track with this.