My understanding is that the purpose of the off switch is to disconnect the battery from everything so you can put the device in storage. The battery cannot charge (or discharge, much) when it is disconnected. This function is necessary so that the battery doesn’t become permanently dead in the store/warehouse before the device is sold to you. Adding in the feature as you describe it would cost more – profit margins on this kind of device are razor-thin so this is not likely a viable product – and there’s not much demand for garden lights in winter, so economies of scale would be difficult to achieve.

You could design it yourself to work the way you want though! It would not be that hard or expensive, probably you could fit it in to your current devices. A few ideas come to mind, although they all require some OK programming skills and basic PCB design skills.

These devices also tend to be highly cost-optimized – as a ‘cheap hack’ you could try taking two apart and putting both panels on a single device (in parallel, NOT in series. Be sure to observe polarity). It’s very likely that the panel and battery capacity are engineered to be just barely enough to serve as a summer garden light at the latitude of the target demographic (again, razor-thin margins). This is most likely the fundamental reason the light does not behave the way you want it to.

An additional consideration is that the performance of many rechargeable cell types decreases with temperature.

Anyway, I hope that, er… sheds some light on the issue!