They are still very small, so I would put them in the conservatory. Try to position them away from the main heating source as they will be fine in a frost free environment. Pot them on in Spring and remember to harden them off thoroughly before planting them out. This will involve putting them in and out of doors morning and night for 2 weeks and then leaving them outside in a sheltered position for another week.

Many thanks.
I'm thinking of buying a mini greenhouse, the sort that are about 80cm wide, 150cm high with shelves and a plastic cover; but I think I'm right in believing that they do not provide protection from frost?

No, they are good for a bit of weather protection but hard frosts and freezing temps will get in. I have one and small plants that are hardy such as seedlings and well rooted cuttings come through winter much better for the extra cover. Do make sure that it won't be sited in too windy a spot. Mine blew over twice one winter so now I have bricks in the bottom and a bucket of rainwater wedged at the front!