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Some Shadu-like pepople(We call them Jogi,) also travel around while begging, but they are not real Shadus like in the discussion here. We can not see real Shadus all the time because they do not appear publicly,otherwise they spend their time meditating and Worshiping Lord Shiva.

do they do that in a temple or do they have their own houses or do they live outdoors?

People say they live in caves on Himalayas, but I am not sure about that. :). People also believe they live for hundreds of years with special ancient meditation and yoga until they get Mochchya.

maybe after the festival they cut their hair take a bath and go back to their corporate jobs. ;)

You can assume it's not possible when you see them and their lifestyle in real, however there is always possibilities of some frauds...