Yes, I think its cold damage also but I wanted to make sure you were not developing root rot. If the damage is only one layer deep, its cold damage. If it was a pie wedge into the plant, it would be root rot. I never give the answers ahead of time though because I want your unbiased answer.
No, don't turn it. Make sure the same side is facing out all the time. Plants adjust their growing habits based on what side faces what direction - don't confuse.
If the previous owners had the plant for that long and gave you their care instructions (including putting in the garage in winter), it should work. Don't prune anything right now - let those brown spots dry (by spring, they should be nice and crispy) back on their own then cut them out next spring. Don't water anymore this winter. Don't put a light on the brown spots but if you want to supplement light on the green part, the plant would probably appreciate that.