Did human-caused deforestation impacted climate and rainfall patterns in the past? I'm asking this because I don't know much about the impact of forest cover loss and evapotranspiration on global climate.
Deforestation does impact climate change and rainfall patterns. A study in 2018 outlined some of the feedbacks, firstly the direct effect of releasing CO2. Changes in evapotranspiration from deforestation caused 33% of the observed increases in the temperature of the hottest days in regions with at least 15% deforestation. There can be a counter factor in that land albedo can change with deforestation, potentially reflecting more energy back to the sky.
The potential feedbacks are further developed in recent work on the Amazon. The direct feedbacks of deforestation on reducing rainfall were small relative to global changes, but cumulative effects can be large. There is no reason not to think that similar feedbacks will have operated in historical contexts.