I have to say that my knowledge of this is from the basic physics and a bit of reading around, so if someone has better information I would like to hear it.
IR is emitted from the surface because snow, ice and water are opaque at that wavelength (11 micrometer) and emissivity is pretty close, though higher for fine freshly fallen snow than for bare ice, so I doubt you could easily "read" snow cover from this data.
Snow surfaces should change temperature more quickly than bare ice, and with warmer water below the ice, snow surfaces would be colder in cold air and clear sky. But that depends on rates of heat transfer (wind) how quickly air temperatures change, so I doubt this helps. My guess is that there are just too many unknowns. Fog and cloud add further obstacles (absorption and emission by water vapour is low at that frequency so there need to be liquid droplets to obscure the surface emission)
I don't know enough about the microwave emission picked up by AMSR, but emissivity does depend on the state the water is in, that is why it can be used to distinguish ice from water. I haven't yet found information about the effect of snow. In the data shown on worldview temperature has an effect as one would expect, we are looking at thermal radiation from the surface. You can see that in rapid changes in changing weather conditions (but again clouds, i.e. thicker layers of waterdroplets can change what we see) Whether the persistent patterns which can be seen are caused by ice temperature (relating to thickness), snowcover, or age (structure, salinity?) I do not know.
One place I am keeping an eye on is north west of Franz Josef Land where a large area which appears blue in AMSR is drifting towards open water. The weeks to come may tell us more about how resilient i.e. thick this ice is.
