Do any of the ancient Hindu/Indian texts mention the importance/unimportance of physical activity/exercise in one's life?
Yes, the 'Yoga-Sutra' by Patanjali and other scriptures on Yoga lay emphasis on 'Asana', which are alternatively called yoga-Asanas.
The eignt parts of yoga are
yamas cha niyamascha eva Asanam cha tathA eva cha/prAnAyAmas tathA gargi pratyAhAras cha dhAranA/ dhyAnam samadhi retAni yogangAni varAnane// ( yogi-yagjnavalka,(1/45). So the eight parts are yama, Niyama, Asana, PrAnAyAma, pratyAhaAra, DhAranA, dhyana and samadhi.
Asana is defined as
sthirasukham Asanah (Yoga-Sutra,sadhana-pAda,46).. So what makes one sit comforably and being still is Asana.
Practice of Asana and PrAnayAma are both involved with physical activity/excercise.