I warm up by asking my kids what they did over winter break and telling them about my vacation and my resolutions for the year.
Remember to write examples on the blackboard and have them start with "I want to..." It's a great activity for all grades as you can easily tweak it according to their levels. (i.e. 3rd years should add a reason, 1st years can keep it really simple.)
I usually like to have my kids share with the class at the end. I ask one of them to share one of their classmates' resolutions -- e.g. "Mayu-chan wants to sleep at 10pm every night." Then Mayu-chan will share, and then the next student, etc. It's fun and engaging, even for my most quiet classes, for the students to be able to express themselves in a structured way.
New Year's Resolutions = shinnen no houfu or shinnen no mokuhyou