What they were doing was very risky. Soon Petyr will send his guards after her. "They will kill Jaime and give me back to Littlefinger. Or maybe they will kill me too". She was afraid, but she keep following Jaime.
It was so dark and so cold out there. A part of her wanted to come back to the safety of her bedroom and stay there forever, but she keep following him.
The last person she should trust was the Kingslayer. "He is an oathbreaker and a Lannister". Perhaps he was taking her to King's Landing and not to Winterfell as he promised, but she keep following him.
"I am his last chance of honour, and he is my last chance of freedom. I have to follow him."