Just as electrons exist in a "cloud", whole atoms and molecules do as well. The classic double-slit interference experiment has been performed with deuterium atoms and even molecules massing more than 25 kDa, such as tetraphenylporphyrins with fluoroalkylsulfanyl chains.

Then given that position and velocity of a particular hydrogen cannot be determined precisely, they could be interchanging continually -- though calculating the probability of such interchange is decidedly (no pun intended) difficult.

As a similar phenomenon, I find amazing the simple, inexpensive, Esaki or tunnel diode, in which electrons cross a barrier (well, disappear on on side and appear on the other) by quantum tunneling. Is that not happening to the hydrogens in different positions in ice?

Just as electrons exist in a "cloud", whole atoms and molecules do as well. The classic double-slit interference experiment has been performed with deuterium atoms and even molecules massing more than 25 kDa, such as tetraphenylporphyrins with fluoroalkylsulfanyl chains.

Then given that position and velocity of a particular hydrogen cannot be determined precisely, they could be interchanging continually -- though calculating the probability of such interchange is decidedly (no pun intended) difficult.

As a similar phenomenon, I find amazing the simple, inexpensive, Esaki or tunnel diode, in which electrons cross a barrier (well, disappear on on side and appear on the other) by quantum tunneling. Is that not happening to the hydrogens in different positions in ice? See this question on proton tunneling.