I used fleece covers pretty much from the beginning
I'm not a fan of PUL covers at night as I prefer something more breathable at night when they sleep longer. I didn't use wool covers until bub was around 5-6 months when she started to wee a lot and I need something mega leaking protection.
But there shouldn't be any reasons why you can't use wool or fleece on a nb overnight. To be honest, I wouldnt bother with wool covers for the first few weeks (or even months) when they feed every 2-3 hrs and you have to change them that often anyway. See how you go, but you can always start out with whatever you like and work it out from there