In an AC, why does a low refrigerant condition cause the evaporator, and/or suction line, to freeze up?
It's all about the temperature/pressure relationship, and how pressure affects the boiling point of the refrigerant. As the pressure of a refrigerant goes up, so too does the temperature and boiling point. When the pressure drops, the temperature and boiling point drop as well. Air conditioning (and some heating) systems take advantage of this, to cool (heat) the air inside a building.
In a normal system, The compressor compresses the refrigerant vapor. This causes the vapor to be both high temperature, and high pressure. The hot vapor moves through the condenser coils, where some of the heat is transferred into the outside air. When the vapor finally comes out of the condenser, it's a hot liquid. The hot liquid moves through the liquid line, into the building towards the evaporator coils. Just before the hot liquid refrigerant reaches the evaporator, it's forced through a metering device. The actual device used depends on the system, but capillary tubes are common.
When the hot liquid is forced through the metering device, the pressure drops substantially. The pressure drop causes the temperature and boiling point of the liquid to also drop. As indoor air is forced over the evaporator coils, the cold liquid refrigerant in the coils absorbs heat from the air. The heat causes the refrigerant to boil, which changes it to a low pressure vapor. When the refrigerant reaches the end of the evaporator, it's a cool vapor. The cool vapor travels down the suction line, and back to the compressor where the refrigeration cycle can start again.
When the refrigerant in the system is low, the pressure; and therefore temperature, of the refrigerant will also be lower. In a normal system, the temperature of the refrigerant at the beginning of the evaporator will be right around the freezing temperature of water (32°F). As the indoor air moves over the cool coils, the moisture in the air will condense on the coils. This condensation will drip harmlessly off the coils, and into the condensate drain.
When the refrigerant is low, the temperature of the refrigerant at the beginning of the evaporator coils will be colder than the freezing point of water (less than 32°F). Because the coils are so cold, the condensation that forms on the coils will freeze. As ice builds up on the coils, it restricts the air flow through the coils. Because of the restriction, the refrigerant can't absorb as much heat from the the indoor air moving over the coils. This causes the refrigerant to boil later in the evaporator, which causes ice to form further along the coils. This situation continues to progress, until the whole evaporator is a block of ice. Once that happens, the refrigerant will start to boil in the suction line. This cause the temperature of the suction line to drop, and just like in the evaporator, cause the condensation to freeze.
Eventually the freezing works its way all the way back to the compressor, which is where the trouble can really start. If allowed to operate in this condition for too long, liquid refrigerant can make its way back to the compressor. If this happens, the compressor can be damaged.
It should also be noted. Once the refrigerant level drops too low, the system stops working. So this problem only occurs in a "sweet spot", where the refrigerant is low, but not too low.
First some background. The HVAC consists of a closed refrigerant loop. At the outside of your home will be a compressor and coils. The compressor compresses the refrigerant and the process of compressing it forces the refrigerant to give off excess heat which is exhausted out the coils. Inside of your home is an evaporator unit with coils. The refrigerant passes through a narrow opening at which point it expands on the other side as a gas (think of a spray can). The process of converting to a gas absorbs heat from the coils (which have the return air passing over them on their way into the ducts).
When the refrigerant levels run low, there are different ways of understanding this impact. I've seen it described that there's less refrigerant there to absorb heat from the home and the closed loop gets too cold after exhausting the little heat it does gather outside. But to me it makes more sense to imagine the effect of the pressure drop in the evaporator coils. The more the pressure drops in those coils, the more extreme the temperature difference as the refrigerant expands to a less and less dense gas. But keep in mind that you still have less refrigerant moving the heat, so while the refrigerant that remains is colder, it's also less efficient.
Additionally, that lower temperature refrigerant comes with a downside. Once the coils drop below the freezing point, moisture in the return air that's passing over the coils doesn't just condense and run out the condensate drain (think of a cold drinking glass on a hot humid day, your coils look like that normally). Instead, that condensation freezes until it's a solid block of ice and no air can pass through. This same problem can happen if you run your HVAC when the outside temperature is too low, so much heat gets removed by the outdoor coils, that when the refrigerant runs through the evaporator is gets below the freezing point. This is why it's very important to not oversize an HVAC for your home, it will cool the air too quickly and result in freezing, and it will run for very short periods of time but not remove enough moisture due to those short run times, leaving you very humid in the summer.