By all means take your son to a women's march. He'll be thoroughly bored, and more importantly, he won't learn a thing. 

A "women's march" to protest the inauguration of a President in a foreign country is nothing but an exercise for yourselves. It won't accomplish anything. No American who voted for Trump is going to reconsider their choice because a bunch of ladies went for a walk in the snow. 

Your son won't learn anything because the context of  women going for a walk in London to protest politics in the US is way beyond a 4 y/o ability to comprehend. 

But go nuts. Bore your son to death with your walk. It might help you sleep better at night if you delude yourself into thinking you did something.