I live in a 1960s-built single-story ranch in Ohio. The house was originally built with a covered back patio, floored with concrete. At some point, the original owners closed it up into a large sunroom.
The sunroom conversion was done extremely haphazardly - the exterior siding doesn't match, carpet was laid with no padding on the concrete, the hood in the kitchen vents into it, and the walls are uninsulated and undrywalled - wainscoting panels attached directly to studs. I don't know what the plan was, but at some point they must have been tired of it being so cold back there because they added a woodburning stove in the middle of the room (without properly screening off the chimney, so a few times a year a starling or a squirrel falls in and either breaks their neck or starves to death) and it must have too hot as they also ran wiring to install a large through-wall A/C unit.
I'm sure it's obvious from my description but the room is impractical to use as anything but storage at this point. In the winter, it gets colder in there than in my garage but I'm not about to run that woodstove and burn my house down, and in summer it's so leaky and humid from the poorly installed a/c unit and ancient single-pane sliding windows that every attempt to habitate it has resulted in having to clean blue mold off the walls and furniture in there. Thankfully the old patio door seals it all off pretty well, and that's what we've done for the last few years since we realized just how bad the situation in there was.
I'd like to make the space functional again, especially as it would increase my square footage by around 40%, but don't really know where to start.
In addition to the other advice, if it is reasonable to do so, you would benefit from raising the floor up a bit to add insulation and a vapor barrier. The concrete will draw in the cold and humidity.
How do you mean, raise the floor? I believe the concrete patio floor was poured as part of the foundation of the house.
I don't know the building code for your area or if it would even work with the other stuff in the area, but the idea is to lay at least 2x2's every 16", put Styrofoam between the 2x2's, lay plastic or tyvek or some vapor barrier over it all then lay down plywood and carpet on top of that. It's a lot of work to retrofit this into an existing space, but if you're starting over, it may be worthwhile.
I had a townhouse on a concrete slab and in the winter, the cold would transfer through the concrete to the point that when it was below 0F, the water lines running through the concrete would freeze up.
I think this is a good idea but I don't think it'll be workable for my space unless the entire structure comes down.