Re: Heating/cooling for small addition
A heat pump is the best option in your climate. A good quality minisplit unit like a Mitsubishi or Samsung is a great option. Mitsubishi units with Hyperheat can generate maximum heating down to something like 0F.
9000BTU's is the smallest unit they make, but at low speed the delivered output is a little lower and they do great job of removing humidity. So you're dehumidifying as much as cooling.
With an average of R10 insulation, the heat loss is about 4000 BTU and heat gain around 3000BTU depending on shading.
SO the unit will be large, but not terrible.
So AC or heat from yur existing system, you'd need to get about 140CFM to the room. That's a 8" duct with two 4x10" registers or a single 4x14" register.
1925 Two-Story Stucco Beaux Arts Neoclassical