It will not do any damage to the batteries (connected properly), I leave my two 6V deep cycle batteries connected to my 12V minder/charger all winter. I have the batteries on a workbench in my garage.
Bob
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2016 GM 2500HD 6.0L/4.10
2018 Jay Flight 24RBS
2002 GM 2500HD 6.0L/4:10 (retired)
2005 Jayco Eagle 278FBS (retired)
1999 Jayco Eagle 246FB (retired)
Reese HP Dual Cam (Strait-Line)
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