Vilya was the Ring of Air, Nenya the Ring of Water. If any of the Three gave its wielder special power over water, it would have been Nenya, not Vilya.
But this leads me to another question. This thread, and the one about
Nenya and the Elessar, have made me think a bit about the specific virtues of the Three, in other words the nature of the power each of them conferred on its wielder.
Each of the three is named after one of three elements - Air, Water, and Fire; at first glance, this looks like they gave their wielders power over the respective elements. Now Gandalf, who had Narya, certainly showed exceptional skill in the handling of fire (fireworks,
naur an edraith ammen, wielder of the Flame of Anor etc.), but being an incarnate Maiar, he certainly didn't depend on a Ring for this; as for Elrond and Galadriel, I don't see them controlling Air and Water in any obvious way. So what does it mean?
In esoteric thought, the four elements are associated with different faculties of the human mind/soul. Applying these associations to the Three Rings, we get:
Vilya - Air - reason. The chief role of Elrond in LotR and
The Hobbit (apart from his being a great healer) is offering counsel, giving advice to others based on his wisdom and knowledge.
Narya - Fire - will and passion. This is the most obvious correspondance: Círdan gave Narya to Gandalf 'for the kindling of all hearts with courage', to strengthen their hope and determination to oppose Sauron.
Nenya - Water - emotion, intuition, the subconscious. This is the least obvious, but (to me at least) it somehow resonates with Galadriel's love and yearning for timeless beauty, as well as the scrying power of her mirror.
I'm not saying any of this was on Tolkien's conscious mind, but it seems to fit, and it may be worth considering if we speculate what use 1st age elves might have made of the Three.