RAW - You might still take damage
First thing to understand is that the Ring of Water Walking does not, RAW, cast the Water Walking spell because it does not say that it does. So, based on the rule that things do what they say and nothing more, Ring of Water Walking would not render the surfaces you walk explicitly harmless.
However, a DM would have to adjudicate how solid acid would actually behave. A DM could rule that it would reduce or eliminate the damaging effects just because it has solidified.
Also a super strict reading of the effect might conclude that "ground" means normal earthen walking surface. In this case, normal earthen walking surfaces do not usually cause acid damage. (thank you @Nick Brown for the suggestion)
It seems to be that the Orb refrains from freezing the liquid if it is cast underwater.
The intention seems to be that throwing the orb underwater wouldn't be considered striking the water. Striking usually refers to as one thing coming into contact with another, with the intent to hit, and when your orb 'strikes the body of water' isn't clear. It is also IN a body of water, so the orb isn't really capable of striking a body of water if it is already in one.
If the globe strikes a body of water or a liquid that is principally water (not including water-based creatures), it freezes the liquid to a depth of 6 inches over an area 30 feet square
Emphasis mine.
While getting into a bit of semantics depth is the distance from the top of something to the bottom. It would be slightly unintuitive if one could consider something 'the top of' if it started in the middle of something, such as the ocean or body of water you are in. Depth doesn't seem to apply properly in this scenario.
If it froze underwater using area and depth would be an inconvenient way to do things.
If the intention of the spell was to properly freeze while cast underwater it would, for more ease and out of a normal expectation, probably freeze in a radius or a more spherical shape. The wording of the spell seems to indicate it is made to freeze the surface of water. It is measured in area and with depth included, not a measurement and description you would use for underwater (at least not normally).
With this and the phrasing of 'strike' and with the observation that the area the spell freezes is an 'area' (with a six inch depth) it can be argued that the orb would not instantly explode with contact with water, if it were already underwater. But further on...
It would not freeze any water.
The freezing of the water is not directly related to the cold damage the spell does. With the orb not properly preforming it's second function, the freezing of water, there is no reason that the freezing would take place. Cold damage does not freeze water without DM intervention (or a certain effect says so, like with the case of some spells like Wall of Water).
Lastly...
There is no difference between casting the spell or taking the orb and throwing it.
It shatters on impact, with the same effect as the normal casting of the spell. You can also set the globe down without shattering it. After 1 minute, if the globe hasn’t already shattered, it explodes.
Emphasis mine.
Outside of a slight word difference between 'explodes' and 'shatters' the spell functions the same whether you are throwing it or casting it and throwing it instantly as apart of the spell. There is no difference between the orb shattering or exploding in a body of water. As long as the orb doesn't strike the water it shouldn't be.
Perhaps more is needed....
If designer intent was that the spell was to instantly freeze water it hit (or started in), excluding water based creatures such as elementals, then it could be that this interpretation is incorrect. I've tweeted Crawford over the issue to see what the intent is.
Best Answer
The rule clearly states that the effect applies to "any liquid surface", giving "water" as an example. Ice is a "solid substance produced by the freezing of water vapour or liquid water". It is not a liquid. The rule does not apply to ice.
The new rule is significantly different to the old one. It no longer involves "the subjects’ feet hover[ing] an inch or two above the surface", and it removes the only solid substance from the list of examples. This suggests the change was intentional, and was not merely an oversight.
There is no reference to Water Walk in the 5e Errata or in the Sage Advice rules articles. A search for the phrase "water walk" on the D&D site reveals no other articles mentioning it.