When I've planted tomatoes and other similar (tobacco family includes peppers & eggplant) plants too early they languished. Stood there not growing because the soil was too cold and sometimes just withered and needed to be replanted.
That said, it occurs to me that using something like floating row cover over your small bedding plants might help warm the surface of the soil by holding in a little of the warmth of the sunshine, and you can leave it on for a few days at a time. This is just speculation on my part, something I would try if I was planting this soon.
Cold soil isn't the only early-season hazard. Over the past couple of years I've discovered a lot of cutworms in the soil. The first year I ignored them, not knowing what they were, and came out the next day to find all of my tomatoes chopped off at the soil level! I dug around and found the culprits, and realized I'd seen quite a few. After that I made sure to use beneficial nematodes ahead of planting time, and I typically put a little Bt in the watering can when I water them in the first time to knock out any that are still around. I wonder if the cutworms are less of a problem later in the spring, having pupated and departed the garden?
My across-the-street neighbor is an old time gardener who swears you shouldn't plant your tomatoes before Easter. Considering how cold the winter was and how cool the soil is, I suppose that advice isn't bad. I won't wait that long, but one of these days if I find the Super Fantastic variety that I prefer, I'll buy them and keep them in the greenhouse until it feels like the right time to plant.