You can continue to use your wrap or carrier in any weather, as long as you and your baby are comfortable.
A good rule of thumb for layering baby clothes is that your baby should wear one breathable fabric layer more than you are comfortable in, but everyone is different so experiment with what feels comfortable for you.
Don’t over-dress your baby! When deciding how to dress your baby remember that your sling will count as at least one extra layer of clothing, though you may still need to add extra layers on their head and any legs or arms that are not covered by the fabric of the sling. For small babies, keeping them close to your body without thick jackets in between you is the best way to monitor and regulate their body temperature.
In wet weather, you can wear a waterproof jacket or carrier cover over yourself or your baby; since your carrier lets you be hands free you could also hold an umbrella!
