First, natural gas is primarily methane, with lesser amounts of ethane, propane, nitrogen, etc. in it. There often is economic incentive to recover C3 and higher from natural gas, for use as LPG.
In general, separating components of differing volatilities is a matter of how different those volatilities are and of the degree of separation. With a very wide difference in boiling points (ex. methane from decane), the desired separation may well be done with a single stage (a flash drum). Since the remaining liquid exerts its vapor pressure in the vapor removed, closer volatilities means more impurity of the heavier material in the vapor, and multiple stages (a distillation column) may be needed. Cold temperatures result only from having to do the separations below the critical temperatures of the mixtures present at various points in the process. With very light materials, low temperatures are needed, and typically high pressure is needed to keep the temperatures from going too low, for various practical engineering reasons. The colder you go, the more difficult the refrigeration needed for condensing becomes.
Practical examples of low-temperature distillations are demethanizers and deethanizers in the hydrocarbon area and nitrogen-oxygen distillation in air separation. For a demethanizer, running at high pressure and a temperature of around -150 F or thereabouts, a refrigerant that much colder is needed (such as ethylene), pumping up to an intermediate level, perhaps needed for a downstream deethanizer, which may run at -40 F at the condenser, for which a propylene refrigerant will do. The intermediate level refrigerant in turn will pump up to cooling water. Refrigeration systems are a whole different subject.