I may be wrong to say that water feels colder and I have not done experiment. But this is what I thought:
When you eat ice cream, it is first few spoons of ice cream that feel colder. Then your mouth being cold is less sensitive to temperature or you are kind of used to coldness in mouth so you don't feel next spoons as cold as first one.
In case of ice vs water, what matters is how long is time for heat exchange. If you take ice cube of 8 ccm in mouth and think of all time till it melts, first few seconds are significant for feeling coldness. If you take 8 ccc of water at 0 degree C, lot of heat transfer happens in just a second or two. Water touches entire mouth at one go and hence rate of heat transfer is faster. Hence colder feeling.
Again, this is personal opinion, may be wrong.