I would germinate the seeds indoors and only move out to the
greenhouse after they are sprouted, assuming that frost isn't in the forecast. If you do get a couple of days that are really too cold, you can move flats back indoors until conditions improve, even if this is a major PITA. Warm weather crops, like
tomatoes, will grow slowly if the temps are too cool but I'm talking from a Zone 4 perspective. Here we start plants indoors beginning mid February until early May, depending on the crop.