A couple of days ago I cleaned the filters in our heat pumps. What prompted me to do this wasn't the cold weather, but the visible build up of dust on the casing of the indoor units. It looked horrible. On opening the unit up, it was clear that the filters were well overdue a clean. Eryughhh. But it doesn't take long to do them, and in just a few minutes they're back inside the pump and its throwing out warm, toasty air again.
Aesthetics is just one reason to attend to the filter. The second is that dust clogs up moving parts, which means the fan and the louvre on the front. Getting rid of that dust has to be a good thing in terms of mechanical performance.
But there's also a third reason – one driven by physics. Your heat pump will be more efficient. How does that work?
The basic idea of the heat pump is that it takes heat out of the outside air and shifts it inside. It does it with an expansion-compression cycle, rather like a fridge. Although the air outside might be 0 degrees, it still has heat in it, which can be extracted and shifted inside. The result is that, outside, the air leaving the outdoor unit is lower in temperature than the air entering (to the extent that there isn't a lot that will grow in front of an outdoor unit – event the most stubborn of weeds get frozen out of existence once winter starts), while, inside, the air leaving he indoor unit is of higher temperature than the air entering. Hence the indoor temperature rises.
But pumping heat from something cold to something warm comes at a cost. It's not the natural way that heat will flow. The bigger the temperature gap between indoors and outdoors, the harder it is to pump that heat. That means more power usage in the form of electricity. Heat pumps work really well for small temperature differences (e.g. the outdoor air is 15 C and you want to heat the house to 18 C) but not so well for large differences (e.g. -5 C to 18 C). The unit may still work at -15 C, but it's less efficient – you'll be getting fewer kWh of heat for every kWh of electricty.
What has that got to do with the filter? Well, a dust-clogged filter starts restricting the air-flow through the indoor unit. That means there is less volume of air passing the heating element every second, to take away the heat. If the heating element is still putting out the same amount of heat as before, it means that it must get hotter. It's rather like the fan on a car radiator. The fan doesn't stop the car engine producing heat, but by increasing the air flow it brings the temperature down. So a clogged filter means that the heating element inside the indoor unit is going to run hotter, if it's putting out the same amount of heat. That's bad, since it means the heat pump now has a larger temperature difference to pump heat over, and therefore is less efficient.
(I'm sure the reality is complicated by the control systems that heat-pumps use – so rather than running hotter it may simply pump less heat – but you don't want that either if you want to heat your home.)
So, cleaning those heat pump filters is a good idea, for a good physics reason.