This post is pure speculation. Feel free to contribute to my wacky ideas via the comments down below (click on the lavender link that says "Comments."Seriously. Do it. Good things will happen.)
I don't know what the plot of the upcoming Christmas Special is or what kind of stories we can expect in Season 3. So let's go character by character.
Robert: I had a brief discussion about his character with a friend. You see, we showed another friend Downton Abbey as we were both obsessed with it and that friend asked, "What exactly does he do?" My friend noted that in season 2, we certainly saw that Robert doesn't really do anything.
So where does he go from here? The war is over. He has cheated on his wife. From what I've read online about the period, we can expect high taxes on the estate and--I'm not sure what else. Will Cora find out that Robert kissed Jane the maid?
Cora: I feel like Cora has grown a lot through the war. She was in charge of Downton the convalescent home as well as running her massive pile of a mansion. I feel like her desire to continue working is only natural. She feels useful. I think that she might continue working with charities, such as Isobel's refugee organization or perhaps with the Red Cross. I don't know what her and Robert's relationship will be like.
Violet: She'll just continue being awesome, won't she?
Mary: I'm not much of a Mary/ Matthew shipper, to be honest. I don't think they're ready for one another yet. I actually kind of hope that she marries Carlisle and that, finally, that damned scandal about the dead Turkish guy in her bed--it's approaching 7 years since that happened, you know--will just come out. I doubt that Mary and Carlisle will have a happy marriage, but still, wouldn't that create some dramatic tension right there?
Edith: I want Edith to find a purpose for herself, something she loves and is passionate about. It's been alluded to that she likes to write or likes books or is good at organizing. Maybe she gets a job? Maybe she becomes a flapper?
Sybil: Well, yeah, Sybil is my favorite of the Crawley sisters, so I sincerely hope that she and Tom Branson have a happy marriage, that she is fulfilled in her career choice, and that the Irish War of Independence doesn't do too much damage. Still, though, I think her marriage to Branson will serve to highlight not only Ireland's plight but the changing of the guard for the aristocracy. There simply aren't enough men of rank alive anymore; so if one wishes to marry, it's going to be someone who would have previously been "beneath you."
Isobel: I hope she continues working in the hospital and with her various organizations. Maybe Edith can help her?
Matthew: I want Matthew to grow a pair of balls. Either you love Mary and go after her or you move on. He needs to grieve over Lavinia..and then what? Go back to practicing law? Become an MP?
I'll write my predictions for the servants and others later. In the meantime, how do you think the story will continue? What do you want to happen?