Gas oil & kerosene behave very differently under cold conditions. For instance, gas oil, at 0°C, begins to cloud due to the parafin content within it. When temperatures of -10°C occur, it begins to solidify and block the oil filter. This is known as its gel point. This is where I have come across the separation from kerosene. Where the fuels have been mixed in the oil tank, the heavier parts with more viscosity solidify and block the filter. By opening the filter, you will see that it can contain more gas oil than kerosene, therefore separation. Just because you have mixed the fuels does not change the chemical make up of their components.
The second main difference between both fuels is their viscosity and it too plays a very important part of the fuel & burner. This is why gas oil is referred to as 35 second oil and kerosene as 28 second oil. A given amount of each fuel takes 35 or 28 seconds respectively to pass through a given opening. It is the reason why gas oil requires a much greater pump pressure than kerosene.
In colder temperature regions of the world, oil burners that use gas oil will have pre-heaters built into the ignition process to pre-heat the gas oil before it enters the nozzle, similar to a diesel engined vehicle. They will also take precautions such as insulating the fuel lines, etc. Just mixing with kerosene will NOT suffice.
Whilst on the other hand, kerosene can withstand temperatures of -30°C and generally does not have the same issues as gas oil. The other issue is that kerosene does not contain FAME (fatty acid methyl esther) and as of 1st January 2011, as an EU directive, there has been an increase of 40% of FAME in gas oil throughout Europe. This also introduces a whole other issue/problem and another reason why not to use gas oil in home heating oil systems.