but would I be right in thinking that that will be partially compensated by the fact that, in the UK, cooler weather tends to be associated with more wind?
Well, yes there is some correlation between the cooler times of year and "quantity of wind", but in terms of the extremes that need to be catered for, the coldest weather is typically very low in wind. Look back to December 2010 for an example - static high pressure over the UK (and IIRC, a lot of Europe) leading to naff all wind and exceedingly cold weather. Round here, it barely got above freezing during the day for a fortnight, and was well below freezing overnight. So at least a couple of weeks when ASHPs would mostly be as useful as a chocolate teapot and drawing massive currents due to reduced efficiency - at the same time as windmills being pretty well useless.
Agreed, there is an 'optimum', rather than 'the more the better'.
Yes, each turbine has an optimum wind speed (or range of speeds). Work by some clever aerodynamics experts has progressively widened these ranges over the years so modern mills have wider operating wind speed capabilities. Also, while many earlier mills had synchronous or induction generators and rotor speeds coupled directly to grid frequency, these days they use power electronics so the rotor speed can be coupled to the wind speed which massively increases the useful wind speed range.
I don't know how they do this, but I would have thought that it would be possible to 'partially feather' the blades when wind was very strong, so that they could function close to their 'maximum safe capability', without risk of damage. Is that not the case?
Again - it depends

Fixed blades are simpler and cheaper - both to build and to maintain. Adjustable blades are more complicated, cost more, and have higher maintenance costs. Also, it's not as simple as just turning the blade to match wind speed. If you look along a blade, you'll see a lot of twist - a "flat" blade at the tips which twists over the length until it had quite a high angle from the disk plane at the blade root. Easy to understand - the tip of the blade is moving faster than the root, so it needs a flatter profile to see the same angle of attack relative to the air flow.
It doesn't take much imagination to realise that the twist in the blade is only optimum for one ratio of rotor speed to wind speed. In extreme, it's possible to feather a blade such that parts of it (probably the root) have a negative angle of attack and hence act to brake the rotor rather than drive it.
And as mentioned above, these days with cheap high power electronics, there's no longer a need to keep the rotor speed constant - hence it can be varied (without feathering the blades) to keep the angle of attack at it's optimum. There's a limit to this - blade forces go up (linearly) as rotor speed does, and if the tips go supersonic then noise increase dramatically, and you can get some "interesting" effects.
There's a small wind farm near here where I've been able to go up and have a look around - organised trip with a local engineering society. These are quite old now, small fixed blades, induction generator. When wind speed exceeds a certain level then they have to shut down (which is automatic) - firstly to avoid overloading the generator (and drive chain), and secondly to protect the rotor. This particular design has an outer section of blade that can "pop out" when released, and twists about 90˚ when it does - thus acting as a very powerful air brake. Once the rotor speed is low enough, a mechanical disk brake takes over and locks the rotor.
As an aside, there's a minimum speed below which they generate less power than the ancillaries (e.g. lub oil pumps etc) take - so better to just shut down and shut down the ancillaries.
I continue to be fairly 'impressed'. Now at roughly the peak demand time of day (6pm, total demand = 36.5 GW), wind generation is still slightly ahead of gas ..
We have a steady 'blow' at the moment throughout the UK, strong wind, but not too strong, so pretty well ideal conditions - yet we are still having to call up gas generation. I am not as impressed. Now if the deficit were made up by nuclear, I really would be impressed.
And that highlights one of the problems. It's mostly CCGT that's doing the hard work of matching supply and demand. As the amount of wind capacity goes up, it has a double whammy on the other generators : the bottom of the troughs gets lower, and the variation in demand increases. The operating costs of a gas turbine increase dramatically when following a widely varying load. Thermal cycling takes a huge toll, with stress cracking of the turbine being a big problem - to add some scale, with even a "small" turbine, if you take the upper half of the casing off and put it on the floor, then you can literally walk through it (another organised visit by the local engineering society). And of course, not only is the operator being told to run the machine in the most damaging operating regime possible - he's only getting paid for a relatively small amount of electricity. As a result, many operators have simply shut down, and others have only stayed open due to being given availability payments.
However, our current nuclear capability is essentially running 'flat out', continuously (i.e,. 24/7, every day) - and it seems that increasing that capacity takes many years and lots of discussion/enquiries/protests/politics/whatever.
China has proved that you can build nuclear plants on-time, to budget, and in relatively short timescales. Of course, part of that is not holding lengthy public enquiries, catering to every minority pressure group, etc, etc. Their approach being that "the government" decides what's going to be built, when, and where - and the population simply accepts it or finds themselves in trouble.
But from a talk a few years ago from an industry expert, I gather they were putting up (IIRC) Westinghouse AP1000 systems in around 5-6 years from cutting turf to producing power - with several in progress at the time.
Most imported energy over the interconnector is French nuclear so low carbon.
That's a "disingenuous" description of the sort usually used by various factions of the green lobby.
Just like over here if taken in isolation, if we import power from France, then that nuclear generated power can't be supplying someone else. So somewhere on the continent there will be another power station opening the taps. That could well be in somewhere like Poland where I believe they still burn a lot of coal. The ONLY time that's not the case, and the power can truly be described as low or zero carbon, is when there is no fossil fuel plant running anywhere on the connected grid and renewables or nuclear would be getting an instruction to reduce output. The European grid is a loooooooong way from that, so it's disingenuous at best to be saying that we import "French nuclear" and it's low/zero CO2.