Depends on how you dress in general, if you dress light and go out immediately after having a cold shower then it's quite likely the case you caught a cold. But then again it could also be stress ¯\_(ツ)_/¯.
Personally, I only have cold showers when the boiler decides to be a tw*t and not work. At first it's hard but you just gotta wet the limbs and then spray the torso, back and head with water as they are the hardest parts to do. From there your body adjusts lol.