It would depend on your area, how warm it is. Tomato plants are very sensitive to frost, so if there is still a risk of even a mild freeze, you'll need to cover them well or they will die. They don't grow well in the cold anyway, so if you have room indoors, I would suggest to wait a little while. Is it warm during the day? If so, you can bring them outside a little bit more each day to weather them and get them ready to be transplanted outdoors. But definitely keep them away from any kind of frost!!!

There is little to be gained by planting most warm-weather crops too early. Soil temperature is crucial - they are not happy campers in soil that is too cool and will usually just sit and sulk (i.e., not develop much below or above ground) until it warms to their liking: about 60 degrees F. in the daytime, 50 at night.

The cold frame not only protects the plants within from cold air, but, if it has been in place for a while, will have also warmed the soil inside up to a higher temperature than the soil outside the frame.

Good luck with your experiment! Hope you'll post results.