Cone of Cold does not freeze water
You already gave the reason yourself:
The spell description doesn't refer to any environmental effects.
And since spells only do what they say, then we know that by RAW, Cone of Cold does not freeze water. Any other behaviour of the spell is entirely up to the DM.
Contrast this with Fireball, which does mention environmental effects (emphasis mine):
The fire spreads around corners. It ignites flammable objects in the area that aren't being worn or carried.
A spell that does freeze water is Freezing Sphere (thanks to @RyanThompson), which says:
If the globe strikes a body of water of a liquid that is principally water (not including water-based creatures), it freezes the liquid to a depth of 6 inches over an area of 30 feet square. [...]
Cone of Cold does not have similar wording and does not freeze water within the range.
Several people, including Pierre Cathe's answer have mentioned that the spell description does contain one environmental effect description:
A blast of cold air erupts from your hands.
The argument is that this could be used to justify a homebrew ruling where Cone of Cold does freeze water. Personally I would not rule this way and here are some of the points I think need to be considered:
- 'Blast' and 'cold' are not game terms. We have no context for their meaning or severity. A blast of cold air to one person could be a "a cool breeze" to another as these terms, without definition, are entirely subjective.
- Allowing this spell to freeze water gives it one of the benefits of the higher level spell Freezing Sphere.
- If it freezes water then it poses issues with underwater combat, line of effect through water and potential difficult terrain.
Overall I think it isn't a good house-rule. Under 'rule of cool' (pun intended) I may allow it once but certainly wouldn't rule this way consistently.