Hi there!

Wool covers would be fine for summer as they breathe - i think fleece covers do too though so they are also an option for you.

You might get compression leaks with wool covers though with a newborn - I know I did. My DD has only just started moving around enough at night to be successful with a wool cover.

I would think that it would be ok to not have a cover during the day at least on the hot days, just change the nappy more often I would say.

Just be aware that flats of any description are really bulky on a newborn and is hard to get good seals against those poo explosions!!!! Have you thought of prefolds? I used a lot of prefolds when DD was really really small (and she wasn't exactly a small baby!!!)

HTH!