Only a little.
Yes ice is made up of water and wind chakra elements, the user will freeze the water by applying wind chakra to it and rotating his chakra around it until the water freezes. This feat can't be accomplished if the user is not a member of the Yuki clan, nevertheless others from the movies were capable of manipulating snow, this for them was a hidden ability much like the Naras(Cries about missing my Nara days). Those were incapable of creating ice only manipulating it.
Now onto the strengths, weaknesses, and neutrality of the element:
Ice is double strong against water, meaning a S rank water technique can be stopped by a B rank ice technique, but you must also take into consideration size and mass. If an S rank water technique that covers extensive range goes up against the B rank version of needles of death it won't stop it since the needles are to small and weight much less than the water technique.
Now for ice and wind, also like you said wind is weak against ice, not much to add on this topic unless you have some questions regarding it.
Now to weaknesses, Ice weak to lightning, simply because the lightning will pierce though the ice and shatter it. Now for earth you are mistaken Ice is not weak to all earth techniques, but only to penetrating earth based techniques such as jagged pillars or weapons of earth, for others that are blunt they are neutral, that is also the case with mud.
And finally to neutrality, Ice is neutral to fire as when a fire and ice technique of same rank collide the results will be as the following: the fire would overpower the wind in the ice technique, but as soon as that happens the water from the technique will cause the fire to get doused. Basically what you said.
Also ice and wood are neutral to each other, just so you know since you have Yamato.
The last thing I would like to say is that ice is versatile like wood release. In ice you can create disks that can help you fly, you can cause blinding through specific techniques, and you can even burn, yes I said burn, you can even burn/create fires with ice. And all the above were in one epic technique

Also shields/armors/pillars/weapons/icicles/monsters/animals can be created though ice release.
Places that help: Wet/damp/humid environments, places that have existing Ice and Snow.
Places that make it harder: Like you said a desert, also in the sea @_@ Yes I said sea, since there is salt in the water.