There's a bit of data in a paper titled A Review of Domestic Heat Pump Coefficient of Performance (by Dr Iain Staffell, Imperial College London, Centre for Environmental Policy, 2009-04) that you could selectively analyse to get a few numbers.
His approach was to collate heat pumps with reported COPs and see how many °C they would boost the inlet air temperature by. Although this information is not immediately useful, if you know you have to raise the air temperature by a certain number of °C to make the internal temperature comfortable, then you can read the charts backward to work out what the COP would be of heat pumps capable of doing it.
In the summary he says: "Linear fits to each data set suggest that COP [of Air Source Heat Pumps] falls by 0.67-1.07 for every 10°C temperature rise."
If you want an easy-to-remember rule-of-thumb, then you could probably just use ΔT/10. Applying that to an example: An ASHP/airconditioner required to pump heat from -5°C (outside) to 20°C (inside) would thus see its COP drop by (20 - (-5))/10 = 25/10 = 2.5.
An interesting consequence of COP reductions of this magnitude is that if the ASHP/airconditioner in the example only had a heating COP of 3.5 to start with, then its effective COP would be 3.5-2.5= 1.0 which is no better than a (direct) electric heater (e.g. baseboard, radiant, wall, bar) anyway. When it's really, really cold outside it might make more sense to turn on an electric radiator, or a bunch of incandescent light bulbs, than run the airconditioner.
Whilst rules-of-thumb are great for estimating things in 'normal' ranges, they aren't so good when you approach operational limits. If an AC's operating range goes down to 5°C then don't expect linear degradation of performance past or even near that limit. Our AC, for instance, actually ices up and stalls at about 3°C — so COP has rapidly reduced to zero (or perhaps even a negative number) at that point. As always, results and observations in the real world trump formulae presented on Internet forums. ;)