Coldness still isn't hate. That is a very powerful term to be used. Chesterton must have had some kind of experience to lead him to a statement like that.
Frost: Some saythwe world will end in fire, some say in ice. From what I have tasted of desire, I favor those who favor fire, but I know enough of hate to say that ice would suffice.
There is a general lack of affection among Protestants for the mother of Our Lord. I call that hate.