The engine has 3 coolant circuits and the heater matrix one is quite small, so you don't need to drain coolant to change it.
When I did mine, I got about 300-400ml out of it (about a Coke cans worth).
Although you do not need to drain the coolant, it is advisable to to that, as it might block your new matrix running `contaminated` coolant. You can drop the bottom rad hose and drain most of it out. The engine coolant system has a few one way valves and other widgets, so a full system flush can only be achieved with specialist tools and software. I never did that - just dumped as much coolant as I could and filled with fresh. You will need to drive it, let it cool, top up and repeat, as some air will usually get into the system. It is supposed to self-bleed over time.
It's easier to do on a fully cold car, as the system will not be pressurised (or hot).