That is just one aspect, and a pretty specific one. I´d be fine with a more general interpretation, in that you will suffer if you dont bring the right clothes for the right occasions. Warm and cozy for cold regions, light and breathing for hot regions, water resistant for rainy weather and so on. The classic RPGs I play, for example, use a system for cold weather where cold DMG is rolled against your character dependant on how cold it is every day/hour/minute, reduced by your "cold armor" (simply put, every warm piece of clothing adds some cold armor). Thus, the better you prepare for cold weather, the longer you can last in it.
But it doesn´t have to be as complicated as that for Sui Generis, especially that bad weather should not simply boil down to a damge over time debuff. Personally, I would already be satisfied if the game simply acknowledged the bad conditions, for example, seeing your character occasinally shiver or blow into his hands in the cold, or wipe sweat of his forehead in the heat - especially if your clothing is inappropriate. It doesnt even have to affect gameplay at all, but just a few little details here and there can go a long way of furthering immersion.
Also, I´m not entirely sure which scale the world of Sui Generis is going to have. I kinda assume it will not span several climatic zones and stick to a rather temperate zone where such extreme conditions are pretty rare, and thus an overly complicated weather-affecting-character system would be a mostly wasted investment of work.