I had this issue in my old house and ultimately had leaks in both the hot and cold water pipes to the washer. If I remember correctly, my plumber replaced the original copper pipes with PVC pipes that could handle a bit of expansion with they froze during really bad cold spells. Unfortunately, there wasn't much I could do to provide better insulation in the first place, but at least the PVC pipes didn't leak or break during cold spells. I just had to accept that I'd have frozen pipes now and again.