The little ice age really started to take hold in Shakespeare's day (late 16th century) and was at its most severe around 1700.
Well, the latest date I could find for the start of the little ice age was about 1500. Most seem to be about 1450 e.g.
http://www.grisda.org/origins/10051.htm
The ones that are later have a previous period called the Medieval glaciation which indicates it was still cold.
Looking at the graph we see a large warm spike that was much warmer than current temperatures at 1500.
regards,
Yelling