In the winter insulation helps home retain heat, which is great, anything which is using energy inside the house is also making heat (you/people/animals, computer, fridge, cooking, hot water, lights etc) so contributing to keeping the interior nice and warm. Sunlight coming in also converts to heat. Insulation doesn't stop heat energy transfer it just slows it down, so all those internal heat gains are compensating for the slow heat loss.
In the summer, that same insulation can slow/prevent heat coming through the wall from outside to inside, but it's not going to help with any of the other stuff. The best insulation in the world is not by itself going to stop overheating in summer if you have internal heat gains and/or solar gain. Shading, ventilation (cross, stack and purge), and thermal mass are key.
Active cooling (introducing actively cooled air/cooled surfaces) is going to be a lot more common in the near future. The regs for London are already different (smaller windows to prevent solar gain) to try to mitigate urban overheating.