According to the main sources of Hanafi fiqh, the answer to the question is that it is Makrooh-e-Tahrimi (reprehensively disliked). (Imam Haskafi – Durr-e-Mukhtar and confirmed by Ibn Abideen in his Hashiya `Radd-ul Muhtar).
However, there is also the opinion amongst some of the Hanafi scholars that it is permissable and the Makrooh element is only when there is no topi or hat worn. If a hat is worn then it is allowed to be left uncovered.
It is always better to follow the safer opinion and ensure that the hat is worn as well as covered.
This is what I have seen from my shuyukh.
Allah knows best [Answer provided by: Maulana Muhammad Salim]