As it turns out, placing nuclear weapons in space is disadvantageous, aside from the prohibitions of the OST. It significantly limits the targets, in space or on Earth, that weapons are capable of hitting.
As to whether ICBM arsenals are militarizing space, I think you would have a different opinion if we were to change contexts. Airplanes are air craft, boats are sea craft, and ICBMs are space craft. That all these vessels begin and end their travels on land, in port, or on the Earth doesn't change their fundamental natures. If the major powers of the world all had massive navies which they almost always kept in port except for occasional training missions we would not be pretending that the oceans were unmilitarized.
> As it turns out, placing nuclear weapons in space is disadvantageous ... It significantly limits the targets, in space or on Earth, that weapons are capable of hitting.
That is only true if you think of traditional applications. There are other uses of nuclear weapons in space, one of which is to create massive EMP attacks. It will only take a couple of Russian satellites in high orbit over the North American continent to fry most of unprotected electronic devices on it. That type of attack will be very hard to prevent and warn against. It is also very effective as it is very disruptive -- imagine most vehicles, radios, cell phones, planes, power plants, water treatment plants being rendered inoperable. Basically if you see this happening, start heading for the closest nuclear bunker.
As to whether ICBM arsenals are militarizing space, I think you would have a different opinion if we were to change contexts. Airplanes are air craft, boats are sea craft, and ICBMs are space craft. That all these vessels begin and end their travels on land, in port, or on the Earth doesn't change their fundamental natures. If the major powers of the world all had massive navies which they almost always kept in port except for occasional training missions we would not be pretending that the oceans were unmilitarized.