How can I create a radiant heat system for melting ice on wood steps?
Electric cables can be fixed there very well. Let's say we use 2 mm thick cables with low wattage (10 W/m).

Firstly you cut 2 mm wide and 3 mm deep cuts to the bottom side of your steps (using a hand circular saw). They should be parallel going from side to side. Put silicone and cables into the cut doing S bends, they should just fit in there. Cover the cuts with silicone to close them against pollution &amp; weather.
Cut one cut for thermal sensor 2 cm next to the cable cut. It should be in a "thermally representative" place. Put the thermal sensor in it and cover it with silicone.
Do the wiring: thermal sensor and cables to thermostat and thermostat to the power line (via curcuit break).

I have in-floor radiant cables installed in cuts in EPS mats under the laminate flooring. There is a thermostat with an in-floor thermal sensor which I set to about 20°C. It works well and feels even better. They say cables must be embedded in a couple inches of cement, sand, or asphalt because the flooring can be overheated. That's why the low wattage (combined with wood stair tread).

But - will it do the job? Sure, because if it's only below freezing, it's enough to raise the temperature a bit to unfreeze. If it's rather cold, it's probably not freezing rain in the air (I don't know your climate).

Main pros:


You can decide how dense the cuts are to each other to decide the total heating power. I'd say 80 W/m2 should do.
Silicone covering the cables (above and under) will protect them from any damage and they will easily exceed the expected lifetime. And the surface of the wood will be stay closed against weather.
You set the thermostat to the required temperature (+3°C maybe). You can even turn it off or buy a thermostat with a programmable clock to be used at night.
Much of the work can be done by yourself and the materials needed aren't expensive too. Even with 100 m of cable and a programmable thermostat you won't exceed the limit.


Some cons:


Cutting from side to side weakens your steps very little or not at all.
You'll have to fiddle with bending and fastening the cables at each turn, because they have some minimal circumference of bend (5 cm maybe). You can let them just bend freely off the cut, but cover them with silicone too. Or cut several short cuts of circular shape.
You might decide to use Thermal Silicone to get even better heat transfer. But I don't think it's needed.


One more thought: pipeline protection cables have a built-in thermostats at certain places. But they are rather thick (9 mm) and expensive.