This is not a credible historical argument, sorry. There were many, many causes of the intellectual developments of early modern Europe (which is much larger than the Enlightenment, which was a relatively late stage of it) that are far more plausible and proximate than "oh people got cold so they started thinking more." It's the silly kind of argument that scientists find amusing but I would be surprised if even she thought this was a legitimate, scholarly historical claim. Much less something that had actual evidence for it.

(This is up there with "the Greeks had dumb gods, so they invented science" argument I have actually heard at least one philosopher make to explain why natural philosophy flourished in Ancient Greece. These are not real historical arguments.)

This is not to say that there weren't effects globally from the Little Ice Age, or that these did not have cultural and historical outcomes. But no historian would support the idea that it was about being cold and staying inside. The Little Ice Age did create food disruptions and those can have huge social, economic, and political consequences. Even then we rarely see these things as single variables (X happened and so Y happened) — the world is more complex than that, and each variable gets thrown into the mix.