Can ice have a higher entropy than water? I've leant that entropy is a state of randomness, and that solids have a more structured form, therefore having less entropy.
However, I saw a YouTube comment stating the following:

a liquid NOT ALWAYS means higher entropy than a solid
  it depends...of the context
  for example,﻿ in the south pole, ice means higher entropy, because Mother Nature sets the equilibrium for liquid water to become ice.

Is there justification for this statement? Is it true that even in a more ordered substance like the ice, there is more entropy?
 A: Let's consider the following situation.  Suppose we have an ice block of mass $m$ sitting at $T=0^\circ\,\mathrm C$ in a container.  To melt the ice, we need to heat it up, and the exact amount of heat we need is the so-called "latent heat of fusion" of the ice, and is given by
$$
  Q=mL
$$
where $L$ is called the specific latent heat and is specific to the melting substance.  The change in entropy of the system during the phase change is, in this case, given by the heat absorbed by the ice divided by its temperature (note here that temperature should be written in Kelvin for the following to be valid which is why we're not dividing by zero)
$$
  \Delta S = \frac{Q}{T}=\frac{mL}{T}
$$
which is positive.  This shows that the entropy of an amount of ice at $0^\circ\,\mathrm C$ is less than the entropy of the same amount (mass) of water at $0^\circ\,\mathrm C$.
I'm not sure what the YouTube comment is referring to.
For more info, see this and this.
A: The youtube commenter was wrong. The spontaneity of reaction (including phase change from ice to water) is not just determined by entropy otherwise petrol would spontaneously turn into water and carbon dioxide without the need to burn
To determine if a reaction can happen spontaneously the Gibbs free energy ($\Delta$G) needs to be $<0$ which is determined by the change in enthalpy ($\Delta$H) as well as entropy ($\Delta$S).
$\Delta$G = $\Delta$H - T$\Delta$S
Although the entropy of liquid water is ALWAYS higher than ice the melting of ice is an endothermic reaction (i.e. it requires energy input). This results in a positive enthalpy ($\Delta$H) so in order for the ice to melt the entropy  ($\Delta$S) and the temperature (T) have to be big enough to overcome the positive enthapy change and make $\Delta$G < 0. It's probably obvious at this point that T needs to be >0 deg C (273.2 K) in order for this to happen
A: we know that every spontaneous process will in the direction of increasing entropy  .  At poles water spontaneously converted into ice  . so  total entropy (entropy (ice+water+surrounding)) will increase
