Wear what you would normally wear - If you need a coat put it on after installing baby in the sling. Dont wrap up baby too much or she will overheat
Take a blanket to wrap round her if you think she might get cold - I suspect you wont get much use out of an overpriced fleecy cover! esp as you cant normally carry a baby in a baby bjorn for that many months
I wear a my normal jacket, which is quite voluminous, and wrap us both up! I also take a small fleece blanket (buggy blanket from Mothercare?) to wrap over ds and tuck him in. And don't forget a hat for LO!