I'm going to move the seedlings into the warm end of an unheated, dim garage (~6 Celsius) for two weeks, then to the cool end of the garage (~4 Celsius) until the end of March. Once the seedlings start putting up leaves again, likely by the end of April, I will move them to a warm location with plenty of light.
This is going to be my first time forcing any plants into "dormancy", so I'm going to experiment as I go along. Usually, I would keep growing seedlings until it is warm enough outside to transplant. I've seen plenty of recommendations for a twelve-week cool period, but I don't think I've planned enough time for that. My bad!
Edit: Edited for clarity.