Summer sheets are normally made out of cotton and aren't water-proof. They're useful for keeping a horse clean before shows, and providing a bit of extra warmth during warmer nights.
LW turnouts are normally unlined waterproof rugs to use during the summer showers, so that's probably what you want!
you can get turnouts with little or no filling, maybe just a cotton lining when you want a waterproof layer but no warmth.
a summer sheet is a thin cotton (or other) rug which you use on a groomed, stabled horse to protect the coat from dust etc., or as a light cover to travel in.
Thank you, one came with my pony when I bought her in August and I've only just started to have a look in the bin bags full of rugs (she really was a spoilt pony) and I wondered what it was for as I want to get a light weight waterproof rug for the summer, a little bit of sun and i think summers here!
I used a summer sheet as a stable rug for my pony when he first moved inside, he was living out with thick stable rug under a heavyweight half neck turnout so he didnt feel the cold in his new stable!