It's the kind of bad answer you tend to get from scientists who think they are being clever (material causes for intellectual developments — not an inherently bad framework, but it can be if you get so simple and monocausal about it) but is not very serious. The idea that people "spent more time indoors" is nonsense and does not take either people back then nor the Enlightenment seriously — it implies that sitting around inside a bit more than before is all that separated people from having or not having ideas about freedom and inequity. It's a silly argument and I find it unlikely that she has really spent any time thinking it through.

There are lots of debates and discussions about the origins of "the Enlightenment," depending on how one even defines that, but it is not something as simple as "people were cold so they stayed inside and then they thought, hey, we should overthrow established institutions and come up with new concepts of human rights!" It's silly.

This is not to say that the Little Ice Age did not have cultural, political, and economic impacts — it of course did, and you could make a more sophisticated argument about the role that these played in the overall context of Europe in this time period. But the formulation you've given is not a serious approach to history.