All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
It is permissible for your husband to wish his female cousins a blessed 'Eed as long as there is no fear of Fitnah (temptation), they only say what is needed to be said, and the women do not speak in a soft, tempting voice. Greeting non-Mahram (marriageable) women on the 'Eed is not a sin in itself; however, the sin is that something prohibited accompanies this greeting.
Shaykh Ibn ‘Uthaymeen said:
"However, some people customarily do what is not permissible in Shariah while greeting others; the male cousin would greet his female cousin with her face uncovered. This is impermissible. It is prohibited for the male cousin to give his female cousin 'Eed greetings with her face uncovered because she is not among his non-Mahram women. Some people also greet their female relatives with their face uncovered, and this is also prohibited as long as the woman is not among his non-Mahram women. Some also would shake hands with their non-Mahram female relatives and this is also prohibited ..." [Majmoo‘ Fataawa wa Rasaa'il Al-‘Uthaymeen, 16/275]
For more benefit, please refer to fatwas 10463 and 83598.
Allah knows best.