Snoo - keeping warm in winter!

Sorry I’m slightly confused. Do you mean when baby is sleeping on a night to have them in a snowsuit as well as a sleep sack? If so the baby would overheat. There are many guides online if you google how to dress baby for sleep.
If the room is cold (think 16/17 degrees) I’d probably do long sleeve bodysuit, sleepsuit, and then a 2.5 or 3.5 tog sleep sack. I only buy 2.5 but I know you can buy 3.5. To put them in a snowsuit on top of that would be pretty dangerous I’d say?
You could always put a hot water bottle in the cot first to heat it up and take it out when baby is getting in

The snoo bassinet used sleep sacks that swaddle the baby, but they're pretty lightweight / not really suitable for a sleeping bag as well.

We've been using a hot water bottle while using the snoo as a regular bassinet, but the baby keeps waking up so we figure it's time to try out the Snoo's features (e.g. rocking baby to sleep) but need to make sure baby is warm too!

Yeah You definitely wouldn’t swaddle and use a sleep sack. I personally would stop swaddling and just use a sleep sack. Or use one of those tommee tippee grobags that’s like a swaddle if you need to transition. I’ve never had a snoo so unsure of it’s features, we just had a regular next to me. I still definitely would not recommend the snowsuit though for night time sleep, regardless of what you decide!
Baby could just be waking up because of their age. How old are they?

Defo no snow suit you'll roast them overnight. Tommee tippee make swaddle bags which are brilliant and come in different togs for colder or warmer weather and then underneath It's a vest long sleeve sleepsuit and the bag and they'll be good to sleep