I've heard this idea floated around a couple of times. [This article] (https://www.sciencenews.org/article/columbus-arrival-linked-carbon-dioxide-drop) describes the idea. As a bonus question, did pre-Columbian Native American societies generally contribute to deforestation more than European societies, or was it just the sharp population decline that pulled down demand for lumber?
I've read a lot about historic climate shifts and I don't think I've come across this theory. Most accounts of the Little Ice Age place its start around the 14th century. In the 1310s there were a sequence of years with catastrophic rains during the growing season, leading to famine, and of course beginning in 1347 there was the outbreak of plague. The other major historical outbreak of what is believed to have been bubonic plague, the plague of Justinian, was also associated with climate shifts. I think the leading theory on causes of the Little Ice Age is swings in the ocean current and air pressure systems.
Brian Fagan has written a number of pretty accessible books about historic climate shifts, here is a link to the one specifically about the Little Ice Age http://www.amazon.com/Little-Ice-Age-Climate-1300-1850/dp/0465022723/ref=sr_1_4?s=books&ie=UTF8&qid=1439153589&sr=1-4&keywords=brian+fagan