Winter layers

Wondering if I can get some advice on what my baby needs to wear when baby wearing. I’m in the UK and it is getting a little colder now. I read somewhere that people overdress their babies so I found a video of someone saying that mum counts as a layer, so does the baby carrier/wrap and so does the mums coat if going around baby so you should dress baby in indoor clothing and boots/socks/hat.

Is this the right advice?

Thanks