Yes, but:
It wouldn't be particularly interesting because Ice would still be a shittier Water, resistance-wise (Water resists Water, Ice, Fire, and Steel, and Ice only resists the first two).
It wouldn't be particularly flavourful because washing Ice with a stream of Water makes it melt faster and most Water attacks come in streams of water.
I say:
Make Ice immune to Ice. It would be the first type immune to itself, which would be a niché.
Make Water moves become Ice-type during Hail, so Ice-types become great switch-ins to Water-types during Hail.
Make Ice resist Ground, because Ground is probably the best offensive type nowadays and cold compacts the ground and thus weakens the earth movements that Ground moves like Earthquake and Earth Power cause or something.
You could also make Ice resist Flying because "Pigeons ramming nto Icebergs", but then Hurricanes would accelerate the melting of Ice.
