You could also 'justify' a max of 10 points of cold damage per turn.
The rule is ambiguous but as I see it the rules intended two scenarios.
The first is moving in water (as nothing is mentioned I assume full immersion). An elemental wants to cross (swim through, dive through) some water and as water hurts it tries to move as fast as possible (50 ft per turn) through it.
The rules indicate that moving through 5ft causes 1 damage, which results in 10 damage per turn at max speed.
The rules say:
For every 5 feet the elemental moves in water
For every 5 feet the elemental moves (at max speed) in water
The second case is about an elemental, that is standing at a dry place (not moving in water), but that's being attacked (splashed at) with water.
In a fight one might throw water skins, that burst, empty buckets over them, etc. In this case 1 gallon is required to cause 1 pt of damage.
I don't see how you can expose an elemental to more water by splashing on it, than itself exposes it to by moving through water (full immersion)
I'd thus limit water damage to 10 points per round
Speed of a fire elemental is 50 ft. A fire elemental moving in deep water could move 10x5 feet per turn and thus have 10 points of cold damage inflicted.
A less ambiguois formulation could be (who knows perhaps there will be revised versions )
A fire elemental moving through or emerged in water suffers 10pts of cold damage per turn (1 pt of cold damage for 5 ft of water when moving through it its max speed)
A fire elemental suffers 1 pt of cold damage per gallon of water (up to a max of 10 pts per turn) when water is being splashed on it
I see that others argue, that moving through water might mean, moving through shallow water (a puddle).
This is not clear (clearly stated). It could also mean, that an elemental does not sink and always floats / hovers over the water on a steam cloud.
or it could mean, that if fully submerged in water an isolating steam layer is forming around the elemental, which absorbs heat, (thus causes cold damage) but also isolates to a certain extent (thus damage is limited) or many other things as nothing is explicitly stated.
As rules are not clear it is difficult to know and the DM has to choose an interpretation, which seems coherent to him.
Coherent does not necessarily mean physically coherent, but which are up to his opinion well balanced in the rule system and which do (if possible) not contradict the wording in the rules.