I haven't had but about two - and not completely successful long term - terrariums, but I'm afraid you're headed for disappointment too.

I don't think your usual seed starting medium will be the problem. The enclosed containers, no drainage holes will be. Time of year may or may not be an issue.

I've always Fall or Winter sown in what I understood to be the 'English' way, so I'm not sure what your thinking was :) Open containers with only a bit of grit for topping, exposed to the weather, drainage. In my weather which should nearly mirror your own, seedlings now wouldn't be a crisis. I may or may not have frost in the next 6-8 weeks, a hard freeze would be unusual until much later in the season if at all, and if one were predicted I would move germinated pots temporarily into my garden shed or garage since I don't have a greenhouse, heated or otherwise.

If you've grown lots from seed, you know that an enclosed environment, no air circulation, inadequate drainage isn't going to work for seedlings. Molds, fungus, liverworts, damp-off in a mild climate. They are going to need air, and drainage....in a damp climate, lots of drainage. I've never given attention to sown, open pots outdoors, have never had them require watering from late Fall into earliest Spring.

If the containers were mine and the potential plants important to me, I'd get those tops off whether you leave them outdoors or move them into your greenhouse. They'd be wearing nothing but some chicken wire to keep the sparrows and chipmunks out. Of course if you do move them in, you're going to be committing to watering occasionally. Do you have a way to add drainage, that might require a third, or fourth hand depending on what type container you sowed in - I use 4x5" deep regular growing pots and don't try to make my own.

The seedlings you describe having already I think would be fine over the next 6 months in your unheated greenhouse if you have room for them there, but you'll need to address those containers.

Thanks, Morz8 - fortunately, it is the work of minutes to poke a hot nail through the bottoms of the containers and whip the lid coverings off. I dunno what was going through my mind - certainly not sense - but, as I often leave plants outside in pots, I usually cover them with a piece of glass until germination (obviously, in a shady north facing spot) and just wondered if the principle could be expanded. I did have a couple of fairly long term bottle gardens (small ferns, hypoestes, etc.) and thought the principle was fairly sound - I was actually more concerned because I had pricked holes in the top thereby failing to maintain a completely sealed environment. However, I am back to my original anxiety - because I have used milkjugs, it is really hard to see exactly how dry or wet the potting mix is (I also have used this mix forever) and feel that a hole just at the top of the jug is not really enough to allow moisture in although I guess I could simply stand the jugs in shallow trays until water uptake occurs. When I have used seed trays, a good soaking is usually all it takes as I keep a clear cover on those too, moving it on or off according to time of year, light levels, water needs etc. and, as you say, the timing is not that crucial as seeds would be exposed to germination potential in their wild state as soon as they drop from the plant - which is never next spring.
One thought, I could simply remove the top part of the jugs, so that I actually have the equivalent of small rectangular pots and shove them all somewhere in the greenhouse.
It is becoming clear that (some)short cuts are simply not worth taking sometimes (especially when the balance of mind is disturbed).

While I can't help you on sowing I do have an idea on moisture levels. Could you not fill one with the normal amount of soil then thoroughly moisten. Now by picking the jug up you could feel how heavy it was and use as a comparison.

SCG