How can you improve brake system performance in extreme weather?

I guess the best would be to first ascertain what the extreme weather is. If in some regions drivers can have summer and winter tyres there is no reason why you can't have summer and winter brake pads. So "softer" pad for colder weathers and "harder" pads for warmer weather. I general, if outright performance is the only consideration; high friction ceramic pad will will almost always be the best option as with high performance comes high heat, and metallic or organic pads does not like heat.

This is one of those small, relatively cheap, aspects of a brake system that is widely overlooked by the average consumer. You can have the best brake setup in the world, if your brake fluid is boiling you will still not stop. Depending on use, I recon brake fluid must be changed or flushed yearly and even more regularly in high demand use. It generally costs less than a set of brake pads and takes about the same time to replace with the right equipment.

In endurance racing I found that heat is a big killer for brakes, generally a larger disc can take more heat but also has more heat to dissipate. Also choosing a grooved disc over a normal one might seem great but it tends to wear down a pad quicker. It is important to keep within the thickness spec of the disc. A set of decent pads and brake fluid is more important than a fancy big disc. In general the disc a car comes out with is more than sufficient to stop and normally has more potential stopping power than what your tyre will allow for. Keeping the disc in its optimal operating temperature is almost the most important aspect.

In my experience, a good driver must be good at adjusting the braking to reduce accidents. Maybe there should be a class teaching this.

Braking technique is a very important aspect. I recon that; as already mentioned; it should be trained, but then should also be practised. It is also something that should be felt, almost as an instinct. You should be able to feel what the car; and in this case the brakes; does when applying the brakes and then you must be able to do micro adjustments to get the most out of your brakes for any given situation. You should be able to feel when brakes start to over heat or when tyres start to slip. In my opinion, this feeling must be introduced to every road user in a controlled environment, so that it does not catch you off guard when it inevitably happens.

In my experience controlling the heat generated is probably the most important aspect of the braking system. Any new car sold has the ability to (without ABS) lock the brakes and so overcome the ultimate friction of the tyres. Just slapping on big discs and thinking you will stop quicker is not going to happen. Being able to have repetitive and reliable stopping power is where the great benefit lies and that is gained by controlling the temperature in all the brake components. The rotors, pads and fluid all have one common enemy and that is heat. Keep that in check and you will be able to more confidently use your brakes for longer.

Firstly, the friction material selection should prioritize high-temperature stability and consistent coefficient of friction to ensure effective braking under elevated temperatures. Additionally, upgrading the brake fluid to a performance-oriented variant with a higher boiling point enhances fluid stability, preventing brake fade. Furthermore, optimizing the design and materials of the brake discs for improved heat dissipation aids in maintaining braking efficiency during prolonged and intense braking events. Implementing an advanced (ABS) with rapid sensor response and sophisticated control algorithms enhances vehicle stability and control, particularly in slippery or challenging terrains.

Using the brakes properly, checking and maintaining them on a regular basis, upgradation of brakes and so on can help only so much. What is most necessary is to avoid overspeeding and rash driving, which are a major cause of accidents in India. Just because you have a state-of-the-art braking system doesn't mean you have to be foolhardy on the roads. Use your common sense and drive safely. Brakes can only help you in a situation that can be controlled by them. Sheer stupidity on the road is detrimental to your health, which we unfortunately see too much of these days. We can't be blaming the vehicle's brakes for this.