On cold nights I would set the heater on on low and dress them warm enough. They have lovely warm sleeping togs at ErgoPouch with a temperature guide.

My girl will wake up if she is too cold but I also use a room thermometer and I have one on her baby monitor so I can see what the room temperature is. My midwife told me to dress them in the same amount of layers of clothing as you plus 1.

An extra layer of clothing more than you would wear, otherwise use a thermometer in the room

Babies can’t regulate own temperature when very young.
Just make sure she’s not under a window or draught under a door.
Singlets are good in Winter on chest.
Just monitor the layers. Overheating not good either. She’ll be fine because you’re on it!

If you think your baby may be too hot one way of telling is if you put your hand on the top of their back just below their necks. It is also a good test if you supect a high temperature. If a baby is cold their cheeks are often cold too.

I think it can really depend on the baby. My first, any slight issue, she was awake. My 2nd in the newborn days was much better and only woke to feed. Both were born in winter. I was always told to check their core body temperature, rather than go by cold toes/hands, as it’s also very easy to overwrap them so they are too hot. I would get a sleep bag/suit designed for the ambient temperature you’re in.