Aren't there trees or a shelter for your horse to go under?
There is a long thread regarding "rugging" horses . IT's been discussed a lot. I would have to say that rugging your horse non stop in hot/rainy weather is FAR worse than having him naked overnight in a downpour. It's summer there, so must be warm rain. Probaly evaporates pretty quickly , no?
I'd say not to worry.
I have heard that in Australia you all rug like uber much. Around here, it's winter and rain/snow, we aren't all that fussy about it. Some do, some don't. But it's much colder than your winter. And folks in Minnesota, I hear they often don't rug at all. Horses are really hardy and manage quite well in the elements.
I know rain rot can be an issue, tho, especially with Thbdss.