I mean if the water can't hurt you it can't stop you from breathing, since that would be "harm".
You are correct. This immunity would not protect from the temperature of super-hot boiling water though. Just the water itself would not drown you, water pressure underwater will not crush you, and staying underwater for long periods of time will not dissolve you or wrinkle you out of existance 
Major Immunity to Drowning is a normal variation of immunity.
Would 'ice' in this instance count as a water based source of damage?
Nope. It stopped being water when it became ice. No wait, that's 4th edition. 5th edition ice is still Aquam. Hmmm.....
The classification between major and minor immunities can vary from saga to saga. For example, in RoP:M, drowning is given as a major immunity. However, in a saga set in a desert, where drowning is much, much less frequent, it would only be a minor immunity.
Now, whether "immunity to water" includes drowning is entirely up to your SG. If you're the SG, then you've got to figure out if the player is "just" trying to claim as broad an immunity as he can (snow, ice, rain, steam, drowning, quicksand, mud ...) or if the immunity makes sense.
Heck, I'll take "Immunity to getting hurt". Or maybe Death Prophecy 
I don't think immunity 'water' would protect you from heat or cold damage, but the physical damage of being hit by ice I would think is a more gray area.
imunity:water will protect you from drowning in water, but not from drowning in say ale... It will protect you from the lash of a magical water-whip, but not (IMHO) from the fall of ice.
Ice might be aquam, but it's not water for purposes of water immunity. I'd say that immunity against ice is usually a minor virtue. (unless you're a viking or have a seal heartbeast )
Most poisons are also aquam, your immunity sure wont protect you.
I don't know if an immunity to water prevents drowning. It's not the water that kills you, it's the lack of air. Does Major Immunity Terram prevent you from taking falling damage?
Immunity to water does whatever the troupe says it does.
If you want it to protect the character from drowning, then it does. If you want it to "protect" the character from drinking, then it does. If you want it to protect the character from ice, then it does. If you want it to protect the character from wine, then it does. This is just one of those things where the troupe has to make up its own mind.
While I agree with the above answer I just wanted to point out that RoP: M gives an example of Major Immunity: Drowning, which should indicate Water does not cover it.
I would say that Greater Immunity (Water) probably should grant immunity to drowning in water (Not quicksand, molasses, or other fluids though). This is mainly because I don't think that water qualified as both "a common and potentially deadly hazard" unless the possibility of drowning is included.
sigh and yet another double-post...
It seems that they need to be more specific on immunities. Immunity to drowning is very specific and covers water, beer, wine and quicksand. Immunity to water is too open ended. Same way as Immunity to terrum. If you want to be immune to most weapons take immunity to iron.
I think an "immunity to water" includes drowning to the extent that the Form bonus for Aquam provides a soak against drowning.
That said, immunity to an element is a pretty major immunity, and I'm not sure I'd allow it (at least, on Storyguide "this breaks my game" grounds) as the immunity virtue.
It is fairly broad, but turn your eyes towards the canon examples of people taking immunity vs. fire, and I feel like a similarly costing immunity to water should be just as broad in effect/usefulness... either that or it shouldn't have the same cost.
It doesn't seem that huge of an advantage to me?
It's relatively trivial for a magus to achieve basically the same effect with wards, and/or effects like Lungs of the Fish. Not that every freshly gauntleted magus could manage it, but one specialised in aquam could do so fairly easily.
Characters having access to effects like this is the game; it doesn't break the game. I'd be inclined to be generous, as storyguide, on what the Immunity Virtue does. Although I'd still explicitly discuss with the players precisely what it does, when they are generating their characters --- so that no player is surprised or disappointed during play.
I would say "Immunity to Water" includes "Immunity to Drowning" but not "Breathe Underwater". You need Air to actually Breathe...
So... if you fall into deep water and can't swim, you'll fall unconscious at some point, but later find yourself cast up on the shore, alive and wet.
If someone forces your head into a barrel of water, you will not die from it, but will gasp back into breathing as soon as you return to air.
It's not a modern view (in which drowning is a form of suffocation - deprived of air) but one that is probably consistent with an ME view...
Sure. That sounds like a sensible interpretation.
If this is a comment related to my mention of Lungs of the Fish above, the point I was trying to make is that almost whatever a troupe decides Immunity to Water to mean, it can be relatively trivially replicated by Hermetic effects. So, I would err on the side of being generous...but you still need to be explicit about what it does and does not do. And what it does and does not do, will probably vary from troupe to troupe. It could even vary from character to character, it would be fine (I think) for two characters in the same saga to have slightly different Immunity to Water Virtues, as long as the players are all clear about what is happening.