You can usually get seedlings going in the Summer without too much trouble by just tossing them in the grow bed. At lower temps you often run into the problem of "damping off" which is caused by a fungus. With damping off the stem tissue collapses at or slightly below the surface of the media. It sounds like you are experiencing either damping off or a lack of light. Lack of light makes the stems weak and leggy. Either one will make the plants collapse but I'm betting it's damping off. Some pics would probably help
.Once the plants are past a certain size they aren't as susceptible to damping off. I'd recommend that you start your plants elsewhere, where it's warm and transfer them into the system when they are larger.