This is a common question. And a fun one at that. But really, it's not the right question. Cold showers can be a source of pride. "My shower is way colder than their showers." Put your feathers down Pea Cock. The right question is, "Am I willing to be uncomfortable for the good of other?" In a world that makes comfort king, that's a difficult question to answer.
In the section of the Exodus 90 Field Guide entitled, "The Gift of Asceticism" there is a section on ascetic acts as penance and a section on ascetic acts as offering. Let's cover each of these here briefly.
Ascetic Acts as Penance. Acts of penance are outward signs of an inward conversion that express contrition and love for God. Practicing asceticism as penance helps you toward a profound conversion. It aids you in making the reorientation of life that you are seeking, (if you are seeking it that is) away from idolatry and toward unity with Christ—from slavery to freedom.
Though, “Interior conversion urges expression in visible signs, gestures, and works of penance,” without interior conversion, “such penances remain sterile and false.” (CCC 1430) We need both interior conversion and outward acts of penance if we want to attain freedom and sanctity.
Ascetic Acts as Offering. A second blessing that comes of ascetic acts is their value as an offering to the Lord for our holiness and the holiness of those we love. The Church calls us to “partake of the prayer and sacrifice of Christ” (CCC 2205). Many of the world’s comforts, though good in themselves, can hinder us from fulfilling this call because they steal our opportunities for sacrifice. A comfortable hot shower is a good thing in and of itself. Yet, when we place the comfort of the hot shower, perpetually in the place of a sacrificial, uncomfortable, cold shower we choose to perpetually trade an opportunity at sacrifice for fleeting personal comforts. Is this a good trade? Are we, as members of the Body of Christ, really getting the better end of the deal here?
If God told you that your friend who is struggling with the faith would encounter Jesus Christ and go to heaven if you offered cold showers for him for the next 90 days, would you do it? Or, would his eternal salvation be too little prize for the cost of cold water?
This isn't pelagianism, this is cooperation with grace. God doesn't need us, but he chooses to invite us into his suffering and allow us, as members of the Body of Christ, to participate in his saving works. That's a huge gift.
St. Paul demonstrates this truth in his letter to the Colossians: “Now I rejoice in my sufferings for your sake, and in my flesh I complete what is lacking in Christ’s afflictions for the sake of his body, that is, the Church” (Colossians 1:24). When our suffering is united to the suffering of Christ “it becomes a participation in the saving work of Jesus” (CCC 1521). The cross brings salvation.
So what's the answer? As cold as the Lord provides you the grace to take up with joy and humility.