The majority of scholars, Hanafi, Maliki and Hanbali, are of the view that the person praying behind the Imam should limit himself to saying: “Rabbana wa lakal-hamd” only, and he should not say: “Sami`a Allahu liman hamidah”.

If the custom of that land is that the best adornment is to cover the head or to pray in a garment with full sleeves, then praying when one is dressed as mentioned in the question is contrary to what Allah has enjoined, even if the prayer itself is valid. But if the custom of the people in that country is to dress as described in the question, then there is nothing wrong with praying dressed in this manner.