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In some regions, summer is cool and there's little use of air conditioning. In other regions, winter is mild and there's little use of heating.
Suppose a household adopted the practice of flying twice a year like migratory birds, living in a cool region during the summer and a warm region during the winter.
Under what circumstances (if any) would the environmental benefits of their reduced use of heating and air con outweigh the environmental costs of the flights?
Firstly, you have to notice that heating is not optional, it's mandatory. If you leave a home unheated, the water pipes will freeze.
So you could perhaps reduce half of the heating bill.
Where I live, my house consumes 10000 kWh/a of heating energy plus water heating (which won't be reduced as water will be heated in the other home too). That's about 3000 kWh/a of electricity if heating is produced using the state of the art technology, ground source heat pumps. The current Finnish electricity system produces around 100 g / kWh of electricity produced, but the emissions are mainly from old-fashioned combined heat and power coal plants that will be retired very soon. If we assume half of load-following power is hydropower and half is natural gas without carbon capture (400 g / kWhe), and 15% of electricity is load-following power, then emissions are 30 g / kWhe. That's 90 kg of emissions for a whole year of heating. Very soon, load-following natural gas power plants will probably use either hydrogen or carbon capture so the emissions from heating will very soon be 0 kg per year because electricity production produces 0 g / kWhe very soon.
I'd say my current house is suitable for 1-4 people, although I currently live there alone. An aeroplane consumes 3 l / 100 km of fuel per passenger. If we assume 3500 km is needed to reach a warm climate during winter, that's 105 liters one way per passenger or 210 liters per year per passenger. Aeroplane fuel direct and production emissions are probably around 3.5 kg / l, so it's 735 kg per year per passenger. Given 1-4 passengers, it's 735 kg - 2940 kg.
You can see that the lowest possible flying emissions (for 1 passenger) are already 735 kg, far more than 90 kg from heating.
Also do note that while a clear pathway to 0 kg of emissions from heating exists, a clear pathway for eliminating emissions of 3500 km aeroplane flight don't exists. Batteries aren't big enough for such a long distance. Maybe if very few people fly, all of the aeroplanes could use biofuels. But if everyone starts flying twice per year, we won't have enough biofuels.
I assume a similar calculation could be done for cases where someone lives in a hot place, and flees to a cold place during summer. Given that the cooling technology (an air conditioner) is simply a heat pump in reverse, I assume the emissions would be very similar, around 90 kg per year.
Even if you used the 100 g / kWhe current emissions, then heating emissions are 300 kg, far less than 735 kg - 2940 kg from flying.
Also I din't take into account that it's realistic only to perhaps halve the heating bill. That would halve the emission reductions from heating too.
So, your plan does not make sense, ever. Not financially (two homes and flying twice every year is very expensive). Not when considering carbon dioxide emissions.
