extension insulation ?

I have a small extension on my house (10 x 12) that gets very cold in the winter. I’m going to replace the windows, but I have a feeling it needs more insulation.

The exterior is stucco over masonry (not sure if it’s cinder block or brick). There is a cellar/foundation beneath the extension.
I poked a hole in the sheetrock to see what’s behind it…I don’t feel any insulation at all, just a small gap and then masonry.
Anyone have any recommendations? (i.e. what would be both effective and affordable, if anything…)
–tear down the sheetrock, put in insulation, re-sheetrock?
–spray in insulation?
–wrap the exterior? (the extension has a new roof so I’m hoping I don’t have to re-do that)

By wolfie |