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.

1. There are 14 pillars of prayer and there are 8 obligatory parts of prayer. There are many Sunnah acts of prayer, both words and actions. 2. The difference between a pillar and an obligatory part is that a pillar cannot be waived, whether one omits it deliberately or by mistake, rather it must be done. An obligatory part is waived if one forgets, and it can be compensated for by doing the prostration of forgetfulness (sujud as-sahw). Learn more in the detailed answer.