Dicky, I used to work as a project manager for an electricity board, not EDF but one of the big names all the same. I lost count of the number of people complaining their electric was going off and some of the excuses they gave for needing their power on was laughable, honestly people who have nebulisers and other medical equipment which means they 'need' 24hr supply yet they live in the countryside in an area we know goes off every time there is a storm, they still don't own a generator for the power cuts

and only complain when the board plans a shutdown.
Tree-trimming is a job that is undertaken all year round, regardless of leaves on or off. The project size is massive, think about it, DNOs have thousands of kilometres of overhead lines and the trees growing through them cause more problems than the public actually know about. These jobs cost thousands of pounds for work that is invariably caused by 3rd parties, besides that the regulator bangs away at the annual profits by charging the DNO for customer minutes lost (an industry guide figure, basically an average of minutes off supply for each customer connected to the network).
If you are that bothered by it then I'd not suggest writing a letter, instead burn the paper to give yourself a little heat, because seriously you are only going to be off a couple of hours and the letter will not get you anywhere. Though I don't recall anyone ever dieing from the cold during a short shutdown in December, though if its any concilation if its that cold the shutdown will be cancelled due to H&S anyway. I guarantee EDF will get at least 10 more complaints than just yours, more if the job is a big one, and even though their pet mouse is having babies (like they would know 3 weeks in advance), Eastenders is on, the village hall is planning a christmas show(sorry love the village hall is on a different feeder and is not off), baking bread in a bread maker, loss of internet, etc. is all irrelavent.
Maybe its not EDF you should be talking to, maybe its the landowner who thinks its a good idea to plant trees in front of the pole to make the view more pleasant, or grow leilandii under overheads. Just be aware that most of these lines have been up since the 1930s to 1950s yet the trees have been there much less, go figure.
Pre-planned power outages are a hinderance, we all know that, but similarly to a car running 24/7/365 it needs to be turned off periodically for essential maintenance. Lots of jobs can be done live-line but the majority of tree jobs cannot so unfortunately people have to be turned off. And as has been said, would you rather they left the job then just when you are cooking your christmas turkey, or opening your christmas presents the power goes off because the trees have finally brought the wires down. A couple of hours on a random Wednesday afternoon is much better than half a day at least when you really don't want it, like Christmas day or at 11:55pm New Years Eve.