Water as a dipole showing the slight charges
You're right - water molecules do have a slight charge distribution across their length. But having different charges makes them attract and repel electrostatically, not magnetically (though I agree, making an ice magnet would be cool... no pun intended!).
The small charges on either end of a water molecule make them behave a lot like a balloon after you've rubbed it on your head. In the latter case, you've caused the electrostatic charges by transferring them from your hair to the balloon. But in the former case, the water molecule naturally has these charges because of the molecule's structure.
Now, if you froze some water into ice while it was in an electric field (instead of a magnetic field), you could align those charges and make an electric dipole in the ice. This is essentially the same as having a charged capacitor, with all of its positive charges on one plate and all of the negative charges on the other. In the ice, those charges would align, leaving you with a tiny bit of leftover positive charge on one end and a tiny bit of leftover negative charge on the other. While you won't be able to pick up paper clips with it, there are some things you can do with an electric dipole - you should be able to get it to attract that balloon that you rubbed on your head earlier!
In order to make a natural magnet, you'd need a material that was made up of little magnetic dipoles (instead of water molecules, which, as we now know, are electric dipoles). Lodestones are one such material - lodestone is a type of magnetite which is naturally magnetic, because the magnetic moments (the magnetic moment is essentially the axis of the magnetic dipole) of the crystals of iron ore in the mineral are all aligned.
Kelly Chipps (AKA nuclear.kelly)
Department of Physics
Colorado School of Mines
Mog from Rainford, UK