Are you sure your widowed friend is upset at the prospect of being alone on Christmas Day?
Last year, I accepted a friend's invitation for Christmas Eve, which is the big day here in Denmark, having lost my husband on 1. November.
It was a pleasant enough evening, but honestly did not feel like Christmas, and I honestly regretted that I hadn't said no thanks kindly to the invitation, gone to church for the four p.m. service, then come home and made my dinner.
If your friend has said that she dreads the prospect of being alone, tell her why you are not able to invite her and ask her which day between Christmas and New Year she would like to visit you.