Heavy clothes and jackets should always be removed before tightening the straps. Extra layers make it difficult to adjust the harness enough (source).
Take the carrier or the whole seat with you inside at night. This way, your baby and the seat both start the journey at room temperature.
Use hats, mittens, and socks to cover your child’s ears, fingers, and toes. Dress your child in thin layers for added warmth without the bulk. A thin fleece jacket is usually a great option. And lastly, you can place a small blanket over your little one.
Never place a blanket or other item over a baby’s head, even if it sits loosely. Doing so could deprive your little one of oxygen.