If you have our kind of weather...

We've had sub-zero weather, including windchills at -12`. As a Californian in the Midwest, we're kind of out of the loop on tricky winterization kinks.
My home was built 1901 and while comfortable, the ground floor water closet at north side of house likes to freeze the inlet line. The heater strip doesn't seem to do the trick. Adjacent sink with separate taps is fine. After a couple 10` days another line supplying a W/C in 2nd story might follow suit.
It's easy to set a slow drip on faucets...but water closets just don't have such a feature.
Until now.
I cut 3 narrow strips of cellophane and put one under each flapper valve, one down stairs , 2 up stairs. They're 1/2" wide, folded over once, so it's about .004 thick; a very small orifice. Too small to clog anything, it causes the level to drop so float will react and refill the tank. Seems to take about 30 minutes.
There are spare strips in each restroom, and since I also rotate which is being used, this may alleviate the problem.

Freezing pipes have been a problem ever since indoor plumbing. Older homes often were made without thought of frozen pipes being addressed. Leaving a faucet drip as you said often keeps them from freezing but usually leads to the replacement of the seat and washer in the spring after the danger of freezing is over. Small price to pay for not having to rip out sections of interior walls to replace broken pipes. Using inductive current by placing 1 lead at the source and the other at the riser to keep them from freezing works as well as long as it is DC current and low enough voltage and amperage as to not melt the solder connections of copper pipes. On threaded galvanized pipes there is the risk of zinc being out gassed into the water through electrolysis hardly a problem on a water closet but any lavatory or faucet which may be used where the water could be consumed it could be. Any type of non metallic plumbing especially PVC but not the new PLEX will burst at the least sign of freezing. and should never be installed in a North outer wall without being wrapped with insulation separate to the insulation of the wall.
Many older homes have little if any insulation in the outer walls but adding a second layer of siding leaving a dead air space between the new cladding and the old siding will greatly add to the insulation of the house overall.
This gets expensive but keeping rooms warm with the judicial use of space heaters facing the walls but placed a few feet away from them is often enough to do the trick in keeping the pipes from freezing the problem with electric space heaters is 2 fold they consume a horrible amount of energy and their constant use can cause the breakdown of the wiring particularly older wiring Any electric space heater even if used to assist in warming an occupied room should be set so it cycles on and off with no more than 40% run time allowing for the wiring to have a chance to cool This holds true even for newer homes plus the heater should be the only device running on the circuit. If the cord ever feels warm to the touch at the plug then the heater is being run on too high of a setting. US standard wall outlets are among the worst designed connection devices in use anywhere in the world.
Our NEC minimum standards is laughable

Another trick would be a continuous circulation system but this would be hard to construct and install when connected to a municipal water supply since it depends on having a pump and storage tank but all risers still become static unless you install 3 way valves and add an additional return lines

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Originally Posted by Frank S

Another trick would be a continuous circulation system but this would be hard to construct and install when connected to a municipal water supply since it depends on having a pump and storage tank but all risers still become static unless you install 3 way valves and add an additional return lines

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Interesting idea, the municipal water utilities would not be happy without serious backflow protection, that is not impossible at all. Why not, boilers/radiators work in a closed loop, on different floor levels and all, with nothing more inventive than a surge tank...

Although being possible as you said boilers/ radiator systems are closed loop. to do a whole house system this is entirely possible but difficult on older construction. One of the houses I lived in I sis a complete remodel I made the hot water circuit a continuous re-circulation system by insuring there were no singularity branches and returning the hot line to the tank reentering on the cold side by means of check valves pressure differential valve a surge tank and a small re-circulation pump and a series of filters on both the house incoming supply as well as the hot water side, any time a hot tap was turned on the supply pressure would be greater than flow the system acted like any other water system. Since the house we have now is on beams I could do this again and may one day
Do a search for re-circulation hot water systems. What I found when I did it many years ago was my water consumption was greatly reduced as I no longer had to run the hot water for up to a couple of minutes for it to reach the furthest tap from the heater.

A good used boiler is one item I search regularly. My building needs ~375k BTU. Already have many, many hundred pounds of iron radiators. The plan is to set them atop braced angle iron 'shelves' around perimeter, single loop.
Here in town is a ex-church with an indoor basketball court, radiators perched in alcoves much higher than players' heads. I wouldn't want to slam into a radiator! Even with immense ceiling height, wonderfully comfortable. One visit sold me on radiant heat, especially with 90 tons of passive iron to absorb warmth.
Walls are 12''+ brick, once I enclose open trusses with drywall, height is just under 16'. Then insulation will be blown-in, R20 to 30 or so.
I've 3 large openings to bridge with 90`fittings, the highest is where surge tank would be. Probably the furnace will house in adjacent wall outside, near ramp leading inside. That seems most likely position to tend boiler, especially if dual-fueled.

I have seriously considered installing radiant heat in the slab of my shop once I get around to pouring the slab that is. If I do I will go the route of laying 100's of feat of urethane tubing in the floor a couple inches below the surface since the slab will most likely only be around 5000 sq ft If I do this I plan on having 5 to 8 zones rather than how I have seen some slabs of that size done with 1 to 3 zones. Hot water systems seem to work better with more zones rather than fewer, I wouldn't plan on having the radiant floor heat do all of the heating for the shop just to keep the floor mass warm enough so as not to feel cold if having to lay on the floor under a truck or piece of equipment the remaining heat could be wood fired. A boiler could be incorporated in the wood fired furnace as well.on my property I have enough dead wood to run a wood furnace for 50 years I might even make it duel to a nearly full passive system by also constructing solar panels and installing them on the roof since the building will have the eves facing east to west giving me at least 2800 sq ft of south facing surface The trick would be to use hot water in the summer by constructing an absorption chiller like a heat pump to condense the Freon in the AC system Again with the size of the possible roof system I could have 2 or 3 evaporators and air handlers about the only energy that would be required to power the system would be a couple of small pumps and the fans in the air handlers. It might take a GOV grant to fund an experimental system but the feasibility of function has sound proven research behind it