Kids do get angry at their mothers if the mom leaves. It doesn't sound like she was much of a nurturing mom, but she was the only mom he had, and she left. That can cause anger if there wasn't anger in the relationship already.
Don't tell your son to love his mom, if he does not, it is just going to make him feel like you are pressuring him to do something against how he feels, and if he does, he does. (And you saying to is not why.) Do see if you can get him some help. Try counseling with your ex if she will do it. See a lawyer if she goes and files a bunch of unfounded complaints against you for domestic abuse. (This would be if she gets as far as making official complaints and you get a letter or notice. Never go to such a hearing without your lawyer.)
Support your son with a lot of love, and assure him all women are not the kind someone should be angry at.
What i meant to say, is that you're a good dad for reaching out here. No one here can know the exact nature of your relationship with your son and your child's mother, however, you are definitely a good dad for reaching out for help here as a start to therapy that is essential, i believe, to help your son grow and become well grounded as an adult.
If it were me, I would ask your ex to attend counseling with you with concern to her failing relationship with her son, and even perhaps you. I don't thin that it's a good idea for you to pursue a relationship with your ex while your son is so unhappy with his mother. While in in counseling with your ex regarding her relationship with her son, your ex is unable to effectively make inroads with your/her son on their own, i would suggest you supervising any contact between them. A family therapist can help you to decide how much contact would be in the best interests of your son, if at all.
And, i think that your son needs to have counseling as well, to understand his emotions with concerns to his mother and what he feels he has missed with his mother, regardless of whether he , with the help of a therapist, can see his way to having a relationship with his mother.
If your relationship problems with your ex has tarnished your boys view, this can be handled with therapists as well, and damages can perhaps be worked on.
i was a child whose parents should not have been together for the sake of the children. The four of us children were damaged , some beyond repair. I grew up fatalistically believing that nothing could (bad) could change and it effected my adult life in many destructive ways. You have a chance that your son can heal, and have healthy relationships in his future.. I think you need to concentrate all of your efforts on helping him to be healthy, even if that means that his mother is not in the picture. As for a women in his life, i think it's important that down the road you're able to show bring into his life a women that can teach him that it's safe to love a mother figure, as it's so important that he learn to love women and not have confusion and frustration be his primary view of women.
I'm glad you posted here, hope it helps. and that you stick around perhaps and find sounding boards that can help you feel not so alone in this process. That's what we're here for.
As for Christmas and New Years, I think you need to arrange for therapy for your child and let him know that you and he will have a therapist to talk to about the confusion and frustration he must be feeling to be so angry with his mom. So that he knows, that change to the way he's feeling is possible, with help. I would focus on change this new year for him. I would maybe choose a female therapist for your son, so that he can have a female adult that he can learn to trust with his feelings.
I'm here if you want to talk privately. You're a good dad for reaching out here. Keep it up.