Does the Fast become Makruh by not covering the hair?
Answer:
If by not covering the hair you mean outside your house in front of strange men then it will be considered a sin. Committing sins whilst fasting will render your fast to be Makruh.
Saaiduna Abu Hurairah 
narrates that the Prophet of Allah 
said: “It may be that the fasting person gets nothing from his fast apart from hunger, and it may be that the one who prays qiyaam at night may get nothing from his qiyaam but a sleepless night.” (Sunan Ibn Majah p.121 v.1)
Only Allah Knows Best
Mohammed Tosir Miah
Darul Ifta Birmingham.