ok ill attempt to answer the temp question . however if someone knows better i will not mind being corrected.
clouds form at high altitude and can change altitude hence fog .
tempratures at higher levels are actualy cooler than close to the earth simply because the suns heat warms the earth and that warms the air close by.
h2o gases rise in this higher temprature until they reach the cooler air where the gasses mix to create water droplets " clouds" . the cooler the high level gets the more frozen the water droplets get . and the more dence the clouds get the bigger the droplets get .
now if it isnt cold enough to actualy freeze these dropplets prior to them becoming to heavey to stay in the upper atmospher they drop as rain .
however if they do get to freeze " and dont become to dence " then it will fall as frozen water droplets known as snow.
As long as the warmer are close to earth isnt to warm it will continue to drop as snow until it lands.
However if the colder air closer to the earth is so cold the air becomes dense then those snow droplets maybe able to float on this layer of thicker air, until it gets warmer and the air thins enough for the snow to fall. Or the droplets become to beig and heavey to stay afloat on the winds.
if the higher level clouds are so dence they freeze the water to a point where the ice droplets freeze hard these can combine on the way down and become hail " gathering more and more frozen drops on the way down and becoming more and more compact.
as for snow at the poles and not the equator , thats simple as its the equator thats closer to the sun than any other part of the planet, and this means the suns heat is more intence here , keeping the landmass and water in this area warmer so any " would be snow " melts on its way down through the atmosphere.