Yes, you can use a baby carrier successfully on a plane. Take whatever wrap/carrier you are comfortable with using. The airport security sometimes asks you to take the baby out to scan the baby carrier. On the plane you have time to sit down, get the babe out if that is desired and get organized. I always tried to breastfeed during take off to help her with changes in pressure. I learned to wait till the plane is not just rolling, but actually taking off. After landing, there is plenty of time to put the wrap on, even if it is a stretchy or woven. You can learn to tie a stretchy/woven wrap in small spaces (airplane seat) quite quickly, but it takes practice. I traveled a lot on buses, so was ok with this. It might be more convenient to use a soft structured carrier (i.e. Ergo, Manduca) with a baby insert - you just fasten the buckles. Mei tai is also quite easy to use, although not every newborn loves them. (My DD got used to a mei tai once she was 5 months, before that she just did not want to be there)
When it comes to getting the baby out of the car seat and into a baby carrier quickly in cold weather, it is doable, too. You can sit next to the baby and pop it inside the carrier and then put your coat on. During the first months she could fit comfortably under my regular coat. Or you can get out, have the wrap pre-tied, pop the baby quickly in, put the coat on , but it depends on the temperature outside. Also, remember, if the space is too small or you really need to be quick, do not worry about doing a perfect tying job (applies to wraps or mei tai). Just good enough to be bring the babe securely to somewhere more spacious and warm to re-tie properly, if needed.
Good luck.
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