So you're saying even though I insulated those last week, we might experience burst pipes again ??
Yes. It will depend on how cold it gets and for how long. Insulation simply slows the movement of heat (or transfer of energy) from the hot side toward the cold side. If it were perfect, and stopped all transfer of heat, you would not need air conditioning until activity inside the house warmed it up to uncomfortable temps.
Insulation is rated in R units and is the inverse of thermal conductivity (k). R = 1/k where k can be btu/unit time.
Copper is a good conductor of heat and electricity, and the heat from the hot water tank will travel up the hot pipe (and to a lesser extent, up the cold pipe, but not as far). Your insulation will slow the heat loss, permitting that heat to travel farther. Letting the water run will bring heat (warm water) through the pipes and prevent the hot pipe from freezing. That running water through the cold pipe will tend to keep the pipe at roughly 55ºF (underground water temp), but if it gets cold enough in your attic for long enough, the water in the pipe may freeze.
My mother's house had the kitchen water pipes run from the basement, through an outside wall into a masonry shed attached to the house, then up through the ceiling into the wall behind the kitchen sink. This shed was on the west side of the house, and cold winds blew toward the house. We tried everything, insulation (wool, fiberglass, foam), heat tapes - every brand, weather stripping the shed, etc, but still had a frozen pipe roughly every three years. This was back in the 1950's - 80's, before really good heat tracing cables became available. The first time the pipes freeze you might be lucky with soft copper - the second time they split.
