do they have a different dressing style?
Yes, South Indian women traditionally wear a "sari", the men wear a "dhoti".
South India
South Indian women traditionally wear a "sari", a garment that consists of a drape varying from to in length and to in breadth that is typically wrapped around the waist, with one end draped over the shoulder, baring the midriff. Ancient Tamil poetry such as the "Silappadhikaram" describes women in exquisite drapery or sari. The sari is to be wrapped around the waist, with the loose end of the drape to be worn over the shoulder, baring the midriff as according to Indian philosophy, the navel is considered as the source of life and creativity. Madisar is a typical style worn by Brahmin ladies from Tamil Nadu. Women wear colourful silk sarees on special occasions such as marriages.

The men wear a "dhoti", a long, white rectangular piece of non-stitched cloth often bordered in brightly coloured stripes. It is usually wrapped around the waist and the legs and knotted at the waist. 
which is the largest state in south by area UNANSWERABLE was this part of india ruled by any colonial power? The Europeans arrived in the 15th century and by the middle of the 18th century, the French and the British were involved in a protracted struggle for military control over the South India what difference occurred after independence here? The region was organised into four states: Madras State, Mysore State, Hyderabad State and Travancore-Cochin.
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South India [SEP] Clothing
South Indian women traditionally wear a "sari", a garment that consists of a drape varying from to in length and to in breadth that is typically wrapped around the waist, with one end draped over the shoulder, baring the midriff. Ancient Tamil poetry such as the "Silappadhikaram" describes women in exquisite drapery or sari. The sari is to be wrapped around the waist, with the loose end of the drape to be worn over the shoulder, baring the midriff as according to Indian philosophy, the navel is considered as the source of life and creativity. Madisar is a typical style worn by Brahmin ladies from Tamil Nadu.