My unit is significantly oversized (it's for a small room and is cooling down a closet-sized space) and because of that, I've never seen ice on the fins. The fan on my unit runs non-stop, too, so even if it were to ice up a bit during a cooling cycle, it would thaw pretty quickly because I'm constantly pulling "warm" air past the fins. I haven't done it yet, but I keep intending to take one of the meters from work and determine the cycling frequency--how often does the compressor kick on and how long does it stay on for. Maybe I'll do that this weekend.
But it's interesting that Sailor hasn't experienced icing of the coils. Question: If target temperature is 55F and humidity is kept at 85% would you experience icing? Stated another way, if you can keep the dew point above the coil (fin) temperature would you avoid icing?
Without trying to be insulting to anyone, I'll explain how all this works just so we're all on the same page. An accurate description of humidity approaches the subject from the concept of partial pressures--the pressure caused by the vapor form of a substance when it is in equilibrium with the liquid form at a given temperature. That's a little confusing for most people, so instead we talk about the air as if it can "absorb" a certain amount of water. At a given temperature we say that there is a maximum amount of water the air can "hold" and if more water gets in the air, it will start to condense out--turn into a liquid. At higher temperatures the air can hold more water, at lower temperatures it can hold less. We discuss a ratio of the amount of water in the air divided by the maximum amount of water the air can hold at that temperature. We call this ratio the relative humidity (RH). By cooling down warm, wet air, liquid water will start to condense out and by heating cool, wet air, the air will start to feel drier.
The study of all this stuff is called psychrometry. Here's a chart that can help determine what's going on in your cave. http://www.truetex.com/psychrometric_chart.gif
You read this chart by knowing a few pieces of information. The dry bulb temperature, at the bottom, is the temperature you measure with a regular thermometer. The RH lines are curved lines moving across and up the page. On the bottom of the chart, find the temperature your cave is at, go up the chart from that temperature until you hit the relative humidity line for your cave's relative humidity. If we use 55 F and 85% RH, we'd be down and to the left of the center of the page, a little below the word "dew". To help keep track of things, I like to mark that point (where my cave is at). If you now go from that point directly to the right until you reach the axis (the end of the chart) you'll be able to see how much water there is in your air relative to each pound of air (not terribly useful for us right now). If, instead, you go directly left from the point you marked, you'll run into the curved top/left side of the chart with the words, "Wet bulb and dew point or saturation temperature" above it. On that line you'll be able to read off a temperature. In our example, the temperature we would hit would be just under 50 F. That is the dew point for the air in your cave. So, if you cool your air down to that temperature, water will start to condense out. This means if your cooling fins are below that temperature (and they almost certainly are when the compressor is running), water will begin to condense out of the air onto the fins. This (now liquid) water on the fins will continue to cool until it reaches the temperature of the fins. If the fins are below freezing, the water will freeze and ice will start to develop. This ice essentially insulates the fins and makes the unit less effective. If the fins are not below freezing, this won't happen...or, if the compressor turns off before the water freezes, it probably won't happen, either because the water will run off the fins and, depending on how long it is before the condenser kicks back on again, will evaporate back into the air.
You can also use this chart to determine how much water is being extracted from the air (and how much you need to put back in the air to keep it at the same humidity), how much energy is being removed from the air, or to determine relative humidity if you don't have a hygrometer (you need two thermometers--one that's normal and one that has a wet cloth around the bulb/sensing portion of the thermometer).
Again, to keep ice from freezing up the fins, you need to make sure the fins stay above freezing (not easy to do--you have to mess with the unit; running the fan at the highest speed possible could also help with this) or ensure the compressor turns off before too much ice has formed (easy to do with an over-sized unit or if a device specifically watches for this--like the cool bot).
Please complete problems 6.2, 4 and 7 for next time when we'll be talking about entropy.