Is this safe ?

In a carrier yeah it would be fine. But you just need to make sure they aren’t super hot. My kids run very hot so I wouldn’t do that unless it was maybe like negative degrees. But you could do that but I wouldn’t make sure they aren’t sweaty. If they are then maybe just do long sleeves and pants and socks. With like a jacket. And then you wear warm clothes and a jacket

It shouldn’t be necessary, and it would make it difficult to position them safely in the carrier and make sure nothing was obstructing their nose and mouth. Remember that baby will be pressed up against you so will benefit from your body heat, and the carrier counts as a layer too. And you can get special coats for parents that are designed to go round a carrier. https://wearmybaby.co.uk/babywearing-in-cold-weather/

Not usually recommended due to risk of over heating as they have your body heat too x

No snow suits are too padded so the carrier won’t support baby’s body properly and make them slump. Also an overheating risk as carrier is a layer plus your body heat

Not recommended to use a snowsuit in a carrier due to overheating. Your body counts as an extra layer for them. I’ve always had my daughter in a carrier until recently and have always just put her in warm clothes, and a cardigan and had an oversized coat, jacket or cardigan over me that I can do up over the carrier to keep her warm xx

Not recommended due to overheating and positioning/ support however I do use a very thin snowsuit and put a single layer of clothes only.