In November I started an experiment to see if it is possible to grow tomatoes - in this case a cherry variety - over the winter period.
I've kept them in a light window and away from condensation that would probably result in a fungal infection.
Not watering too much, that is, keeping the soil almost dry, has also helped in keeping the seedlings healthy.
They are looking a little "leggy" but reasonably good for the middle of December.
Feeding will be unnecessary as the soil has plenty of nutrients and they won't need much at this slow rate of growth. Over-feeding and over-watering are two of the most popular mstakes that are made when growing tomatoes - killing them with kindness you might say!