I don’t know the program but I do schematic design on a professional basis.
For side projects, colleagues now switch to KiCAD, which I haven‘t used yet, I used Eagle as well.
All batteries suffer at low temperatures but as the solar light is only consuming a relatively low current and the solar cell won‘t do fast charge as well, the increased impedance is probably of less concern.
The idea behind my proposal is that protected cells include over- and undervoltage protection, so you could skip the defective circuit.
Otherwise you would have to repair it or design a new one…