Yes, we did it to our 1830s house. The primary reason was the same one you are considering. We went on a major conservation rampage, shortly before utility rates doubled since our home had some major heating issues. Our porch needed replaced and it seemed like the perfect time to install a greenhouse in its stead.

Ours is 12 x 24, has a brick floor and is heated with a gas fireplace. We also have a quiet, commercial ventilation fan at its apex to exhaust hot air, and shade it in summertime. Inside the greenhouse are three (what used to be) exterior doors into the house, and a window. We leave them open to the greenhouse year round with no problem.

Ours is not directly south facing, so we do not get the larger solar gain in winter, but do get it from the west wall in the afternoon. On cold sunny days, we also get it from overhead. The south and east exposures are against the house, as it sits in an ell shaped area. We get a lot more sun in spring and fall, of course, and it has to get pretty cold outside before the heat comes on.

What it does for us, it to provide a windbreak and a dead air space in winter, and that in itself is an excellent insulator. The kitchen stays a lot warmer now because of it, and it's very pleasant in winter, to have a fountain running out there, and ferns hanging outside the kitchen window. Because we are constantly in and out in all seasons, tending the g'houses, gardens and poultry, it also makes a respectable mud room to drop the boots and coats. We sometimes sit out there in winter to read, or have our morning cuppa. When we were doing the energy conservation thing, we got central heat (hot water radiators), new windows and did a lot of caulking and such. It cut our energy consumption for heating almost in half.

May I ask what zone you're in? It would make a difference in how practical using a g'house would be, and how you will need to outfit it. If ours isn't shaded in summer, it gets hotter than Hades in there. That is something to consider.