Assuming you're asking about human skin, not a fictional blubber.
It depends on the depth at which they live
Melanin (a brown pigment found in human skin) is a natural form of sunscreen, it is also the only colouring in human skin (pinker skin comes from oxygenated blood near the surface of the skin).
The graph below shows the absorption of different frequencies of the electromagnetic spectrum. Melanin aims to block UV (the left most section) where we can see that, per meter of depth, water absorbs a lot of this.
So, just as different skin colours naturally developed depending on sun exposure on the surface it would also depend on what depth the mermaids lived (much less exposure the deeper you go as seen by the graph above). If the mermaids regularly swim above the waves, however, they may well need more melanin to combat not just the sun from above but also that reflected from the surface around them.
So if the mermaid needs to surface regularly they would have darker skin, if they live below the surface they would likely be pale skinned.
The answer would be different if you want your mermaids to have blubber other adaptations but, given the question is about the little mermaid, my answer focuses on human skin.