The typical bike tire can't hydroplane until over 100 MPH, so you don't have to worry about that part.
Just be careful with the reduced grip of wet roads. Painted and plastic road markings, tar strips, and metal are especially slippery, as are wet leaves in the road. Brake earlier to clear the rims too.
+1
Your best option for normal but wet roads is getting tires with a slick (no tread features) tire with a grippy compound. As for paint, man-hole covers, gratings..... listen to tsl.... he knows what he speaks of.
Or, you can listen to Sheldon Brown:
Tread for on-road use
Bicycle tires for on-road use have no need of any sort of tread features; in fact, the best road tires are perfectly smooth, with no tread at all!
Unfortunately, most people assume that a smooth tire will be slippery, so this type of tire is difficult to sell to unsophisticated cyclists. Most tire makers cater to this by putting a very fine pattern on their tires, mainly for cosmetic and marketing reasons. If you examine a section of asphalt or concrete, you'll see that the texture of the road itself is much "knobbier" than the tread features of a good quality road tire. Since the tire is flexible, even a slick tire deforms as it comes into contact with the pavement, acquiring the shape of the pavement texture, only while in contact with the road.
People ask, "But don't slick tires get slippery on wet roads, or worse yet, wet metal features such as expansion joints, paint stripes, or railroad tracks?" The answer is, yes, they do. So do tires with tread. All tires are slippery in these conditions. Tread features make no improvement in this.