If traveling in December, buy tickets for the sleeper compartment on the night train to Rovaniemi as soon as possible. Calling is the best way to ensure you book the right compartment. The actual compartment will be assigned no more than 60 days in advance. VR (Finnish Rail) will then email your tickets.
While there is food on some of the trains, it's helpful to bring snacks. Though the train ride is smooth and sleeping is comfortable, the sleeping compartments are small. Store what you don't need in the storage car. There is access to it during the trip if needed.
Any time of the year is a good time to go to Lapland. If you want to see snow and go sledding, then winter is a must.
Children ages 10 and younger travel free of charge on night trains with a parent in the same sleeping compartment if a berth is not booked for the child. You must inform VR that a child will travel with you when buying your tickets. Children under the age of four do not need tickets, but they do need a pass (which will be issued with your tickets). VR can email them to you.