Though climate is one of the driving factors that determine clothing in India, there are other historical and cultural factors that have influenced Indian dressing sense.
Women's traditional dresses in different regions are the best way to research this as they have preserved dressing sense for the past 300 yrs unlike men who had to change for various reasons.
For instance, the dressing style in Rajasthan is not in sync with the hot conditions there.
The best example, the purdah system used in the North Indian culture is mainly due to the historical fact of Muslim Rulers' invasions from the central Asian regions. The purdah culture was introduced by them. That is why in South India this culture is not prevalent because the invaders never came deep down South.
In the same way dressing up in silk material is again not very climate friendly in South considering the hot climates and rare winters. The famed silk sarees or silk dresses of South India are more to do with the social status of the person than the climatic conditions. Silk is expensive when compared to cotton and wearing silk is considered to elevate social status. But since Silk acts as an insulator of heat, it is not at all a good material to be worn in South Indian summers.
The above are just two examples of how factors other than climatic conditions influenced our clothing in different regions. The way saris are worn differently in different regions is due to the fact that there is a lot of influence of the local culture and in some cases it is the simple practicality.
Of course for the normal day to day wear the usage of cotton was mainly due to the climatic conditions as cotton is one of the easier crops to grow in the Indian subcontinent's temperate climate.
Khakis are a best example of dress being influenced by climatic conditions. The brown earthy conditions made the British adapt to Khakis as the regular uniform for soldiers and police in India so that it would act as a good camouflage as well as hide dust and grime on the cloth.