Optech rainsleeve for your camera, maybe an umbrella on a light stand to cover most of it. Or, strap an umbrella to a backpack frame - you'll look like an Inspector Gadget dorkus, but you'll be free to move around the shoot area while staying mostly dry.
Plastic bags over your Speedlights. Big Ziplock baggies, or maybe even clear wastebasket liners.
Cheapo modifiers, if any. They won't melt in the rain, I promise.
I had to wash one of my cheap PBL brolly boxes after the cat took a pee on it. It held up just fine to a vigorous wash in the bathtub. Though, I didn't let it dry fully before putting it away, so it mildewed a little. I should have let it dry for several days before closing it up.
If you use modifiers, put heavy sandbags on your light stands. Where there's rain, there's probably a breeze. Put the sandbags into heavy garbage bags to keep them dry. The light stands are metal; they'll be fine in the rain, just let them dry thoroughly before folding them away.
Backlight the raindrops to get them to light up and freeze in space.
Here's one of my favorite shots of my wife; it's not quite what you're looking for (we were doing a promo shoot for a Halloween show), but you can see the effect of the backlighting on the rain. This is two bare Speedlights on tall stands behind her; refer to the shadows on the ground for cues as to their exact position.
Shooting in a downpour is one of the items on my bucket list for 2014.