We've got a similar problem, but with a slight difference:
We've got 2 Yorkies that go out in the garden as and when they need to, as they use a cat flap in the back door. The only problem is, we have to leave the conservatory door ajar, so they can go through the conservatory door to access the cat flap in the back door. When they come back in they have a nasty habit of leaving the conservatory door open - only problem is, it needs to be pulled shut - I wonder if you could train your dog to pull a door shut ??
Our house is quite nice and warm, but the conservatory isn't used much during winter as it's freakin' freezing ..... I always know when one of the dogs has been out as I can feel the cold air coming in ....