Praise be to Allah.
Yes, a woman has to cover her hands, because the hand is part of the ‘awrah. Al-‘Allaamah Ibn al-Qudaamah said in al-Muqni’, as was quoted by al-Mardaawi in al-Insaaf (1/452): The free woman is entirely ‘awrah, even her fingernails and hair. End quote.
Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him) said: It is proven in al-Saheeh that the woman in ihraam is not allowed to wear niqaab and gloves. This is one of the things that indicate that niqaab and gloves were customary among women who were not in ihraam. This implies that they covered their faces and hands. Majmoo’ al-Fataawa (15/371-372). Thus you may know that the woman is enjoined to cover her hands in front of non-mahram men, but it does not mean that she has to cover them with gloves. She may let part of her garment hang down over them, and if she needs to wear gloves sometimes and it is a little hard for her but she can put up with it, then she should put up with it and seek reward for that, because the reward will be commensurate with the degree of hardship involved, as it says in the hadeeth from the Prophet (peace and blessings of Allaah be upon him).
And Allaah knows best.