Rose, I run in the morning, when the temp here is usually in the mid-30s (F). I find that just getting something that keeps the cold air off the skin is best. It doesn't need to be really think or bulky, or that just becomes restricting. Once you've gotten 10-15 minutes into you run, you'll be warmed up from the exercise anyway. A key for me is a hat to keep my head warm, and that's something that easy enough to carry for the remainder of your run if you become too warm.