Depending on the temperature of the gas cylinder bottle and the rate at which the gas is being used, condensation or even ice will form on the gas regulator.
If we look closer, well realize that nature of the two LPG - Propane and Butane can also be the cause of ice or freezing on gas regulators. LPG is sold in two forms: commercial Butane and Propane. LPG (Propane) freezing point is at -188°c (-306.4°f), which is very low and impossible to attain. Propane does not freeze in winter, which is why it is more preferable LPG than Butane in countries with cold weather conditions. So, this could only means that ice of Propane tank gas regulators are caused by rapid movement of LPG in a gas cylinder bottle. The cause of Propane tank frost and ice on Propane regulator are the same. Under certain temperature, ice and frost can form.
Propane works well in winter, as explained earlier on. However, if you live in cold weather countries, excluding Antarctica, and you get Butane gas - if temperature drops below freezing, the Butane will stop vaporising. Propane tank frost is a result of the tank to boil and vaporise. This makes than tank walls cold, as the boiling occurs at -42°c (-43.6°f). This also explain why hot water is used when testing how much LPG is remaining in a gas cylinder bottle. The visible condensation or Propane gas tank frost line indicates the level of the liquid LPG gas remaining in the gas cylinder bottle.