Rain rain rain is pretty much the norm in the UK where every horse owner owns about 10 rugs/blankets and is always browsing the sale rails for more
If your horse is used to being rugged, then the following applies:
Good rug on when out in the day, make sure it's not getting soaked through - if it is, it's not good enough.
Put that rug to dry overnight when your horse is in, with horse wearing a stable blanket. Put on dry rug the next day.
If your horses isn't used to being rugged, then if he's rugged and hardy and has some shelter, he'll survive anyway. As someone else said, he won't melt!
Very important to have plenty ie ad-lib hay at night to help keep them warm, particularly if they did get wet.