I live and work in earthen houses heated solely by attached greenhouses in a cold climate where winter heating is a major need. It works great and we don't use backup heat. However, we remove the greenhouses entirely in the summer, and put them on for autumn through spring.
Your design does look more like an "atrium" than like a "greenhouse." Horizontal or roof glazing tends to cause heat loss in winter and unwanted heat gain in summer when the sun is high. Making it basically removeable would help a lot. I don't mean opening one of the panels, but opening all four so that only the frame remains, and also opening a significant portion of the south glazing as well for summer. Your vertical south facing front is a good idea, since it gets sun only in winter and not in summer, or only in late summer. However you didn't give your latitude -- the further north you are, the more the sun will still hit your south glazing in summer, and in August if you've got 100F outside and a huge hot window, you may not be able to use your house wihtout a lot of AC. Heatwise, you can design for that, but your plants will want sun in summer as much as or more than in winter (thinking of the natural cycles of plants). In both summer and winter, plants that are not pressed right up against the southern glass won't get many hours of sunlight because the space is narrow and doesn't admit any from east and west. You'll definitely be able to make a lovely living space full of greenery that is thermally helpful in winter, but if you want to produce fruits in there, eg fruits that grow in warmer climates than yours, you may find that they don't get
enough direct sunlight to produce and ripen well.
Adobe does a whole lot to moderate temperatures, and with your fairly moderate extremes of 40F and 100F, adobe alone will do a lot to keep your space comfortable for most of the year with no additional heating and cooling. The south facing glass can easily make enough difference in the winter so that you wouldn't need additional heat: your design is not optimal but with a cool winter it may be enough. The real issue is overheating in summer and fall.