What are they seedlings of?

Cosmos, poppies, schizanthus, osteospermum, morning glory, canary creeper, ammi majus, nicotiana , bacopa and others.

I would leave them for a few more weeks or put in a coldframe/greenhouse if they are quite developed (have normal leaves and not juvenile leaf).

If it came to a push, Poppy, Bacopa and Canary creeper are hardier enough to go out than the others are.

yes they will be ok in the unheated greenhouse. If a hard frost is forecast put a cardboard box/similar over them on the night and then uncover again in the morning. if the forecast for the day is warm then they could go outside during the day and back in at night.

I've already started the greenhouse hokey cokey :o).

Hope I won't be collapsing with the heat in the greenhouse when I'm doing all my potting on !! Been glorious here in Bolton today :-))

Hi,
Have these seeds been sown in seed compost?

If so and they are sprouting up as you say they are, they'll need repotting on asp,
seed compost is'nt made with any fertilizer in its make up,
seed compost is lighter than other compost to enable the germinated seeds to get to the light quickly also seed compost is made to retain moisture rather than a lot of water as the water will rot seeds if they cant get through the compost thats heavy.

The seed pod has the food for the germinated seed for a short while and once its through the compost it needs repotting to a fertilized compost so the seeds can both feed and grow roots,

So you can see why you need to re-pot very soon,
Use fleece to cover the seeds of an evening if you want to take the chance ref unheated greenhousing.