I'm a bit bored.

Assume they turn off the heat. Let's use math to waste some time

Heat loss in BTUs/hr is

HL = U-value * Area of wall (sq ft) * temperature difference

U-value = 1/ <sum of r values of layers>

(U-value is actually standardized to certain conditions, but it's all we've got :P)

A 2x4 stud wall with 3.5 inches of fiberglass is about R-15 (and a U value of 1/15)

IE the wall is 8x20, you would lose (1600*temp difference/15) BTUs an hour through that wall.

How many BTU it takes to raise or lower the air in your house one degree depends on the volume, but it's roughly 0.02 BTU to raise 1 cubic foot of air 1 degree.

Basically, as it gets closer to the outside temperature, the rate of cooling will slow down.

Worst case, assuming you have a 1600 sq ft home (which was average in 1950), and it was only walls (this is the worst case), and it was 35 feet tall (a lot of zoning codes in the country allow 35 feet from top to bottom), and it was square (40 * 40 ft), you have 40 * 35 feet of wall space on each of the 4 walls, or 5600 sq ft of wall space. Assuming it started out at 68, it will initially lose 14187 btu/h through the walls when the outside temp is 30 degrees (and the btu/h will decrease quickly as you lose temperature in the house).

You would have roughly 56000 cubic ft of air in this house (40*40*35), and it will take 56000*0.02 = 1120 btu to effect a 1 degree change in air temperature.

So over the first hour, it will lose 12.6 degrees.

The second hour, we start out at 68-12.6=55.4 and if it was still 30 degrees outside, it would lose 9482 btu that hour, or 9 degrees, roughly.

So the third hour, we are down to 46. If it was still 30 degrees outside, we'd lose 5973 btu that hour, or 5 degrees, roughly.

So the fourth hour, we are down to 41. If it was still 30 degrees outside, we'd lose 4100 btu that hour, or 4 degrees, roughly

So the fifth hour, we are down to 36. If it was still 30 dgrees outside, we'd lose 2240 btu that hour, or 2 degrees

So the sixth hour, we are down to 34. If it was still 30 degrees outside, we'd lose 1490 btu that hour, or 1.something degrees

etc

Again, remember these calculations are very much overestimating the temperature loss because it changes every instant as the temp difference goes down. I don't have mathematica to do this properly and am too lazy to do it by hand.

But basically, after the first day, inside your house is going to pretty closely follow the outside temperature, lagging behind by a few hours.

For the pipe containing your water, copper pipe heat loss for fluid inside 3/4 pipe with a 40 degree temp difference is 29 BTU/hr per foot. So it will take slower to follow the temperature, but there is less of it.

Water takes about 143 btu per lb to convert to ice (this is pure water).

Multiplying it all out, this theoretical house may actually have water freezing after the first day, at night, but its going to be close.

There are other things at play. If it's city water, it will tend to have a lower freezing point due to impurities. Additionally, once you hit back to the line you are sharing with your neighbors, , the heat from that water (at 40 degrees) is going to diffuse through the rest of the pipe/water over time. Same with all the other water that may get over 30 degrees.

All this said, i'd say

1. Its going to be close as to whether anything freezes. If it gets into the low 20's for more than a few hours, i'd be worried. If it stayed 30 degrees the whole time, i wouldn't be worried.

2. I have successfully used math to waste time.