One thing you will need with tonnes of rain is fenders. OK, that's two things. In my experience, the type that wraps closely around the tyre does a better job than a cheesy flap on top of the wheel. But even a cheesy flap is better than nothing.

Sounds like you could take a look at various bikes sold as cyclocross, or CX, bikes. They generally have drop bars, tend to have better mounting options for racks and fenders (and more clearance to fit studded tyres, should you need them), and they won't mind rough surfaces.

--J