I agree with Gav. For an easy solution just put an intake / filter at the front of the motor. Should be plenty of cold air and positive air pressure there just from the air running under the car.
I made up an intake in this style for mine and planned to shroud it so it took cool air from under the car.
With your setup the hot air from the radiator is already shrouded away from the intake.
As for water, with the filter in this position water won't drain into the intake. Any water/spray drawn in from under the car will go through the motor but that's no problem. Motors don't mind a bit of moisture in with the intake charge. It's actually beneficial in turbo charged motors.
Cheers
Mike