There is no reason why you can't keep any of these out of doors in the winter. The two assumptions you will have to make are what is the lowest winter temperature and why are you storing the gas? From this you can decide what you are storing them in.
Methane has a boiling point of −161 °C at a pressure of one atmosphere
Propane has a boiling point of −42 °C
Butane has a boiling point of −0.5 °C at a pressure of one atmosphere
So methane will remain a gas no matter where you are on Earth.
Propane will also remain a gas apart from some very cold places on the Earth, such as Antartica and Siberia. If the temperature drops below the boiling point there are two main problems. There will no longer be a supply of gas for, say, heating. There is an additional problem in that the storage container that may have been pressurised, will suddenly come under a vacuum when the gas condenses to the liquid. The atmospheric pressure may crush the container or cause it to crack. This may not be obvious until the gas warms up, repressurises the container and it leaks.
Butane will suffer the same problems as propane when the temperature drops below -0.5C.
One way around the problem of the gas condensing and generating a vacuum is to pressurise the storage vessel so that the gas is stored as a liquid, i.e. it is already a liquid.
Hope this is useful
Thank you. That helped a lot.