I don't think there should be any thoughts about being perceived wrongly or weakly. In the cold weather dressing up appropriately to avoid catching a cold or a chest infection is important. If this means wearing a sweater or cap with a shawl, there's nothing wrong. We should not think about what others would feel about us for such things. They are not going to come to our rescue if we fall sick and we can't also blame them if we fall sick without wearing sweaters. We always put on the sweaters for our children who leave home by 7:30 AM in the morning, when there's the air is certainly chilled in the mornings. We should not hesitate in such matters and nobody would seriously question us or pass comments, yes, they may joke a couple of times but nothing serious. I've seen people wearing one thin and one thick sweater for morning walks while others come only in a T-shirt, it's an individual choice also.