A cold plunge bathtub is the cheapest possible entry: you already own the vessel, it already has a drain, and a bag of ice turns it into a plunge this evening. It is how a large share of people start, and there are three practical reasons most of them eventually buy something else.
Why it works
A bath holds enough water to immerse most of you, it is plumbed, and emptying it is a plug rather than a pump and a hose. For testing whether you will keep the habit up, nothing beats it: the marginal cost is a bag of ice and fifteen minutes. Many people run this arrangement happily for months.
Adding a chiller
Chillers made for bathtubs exist and work by circulating water out, cooling it and returning it, usually through hoses hung over the rim. The things to check are whether the unit can cool your bath's volume in a sensible time, where the unit will live, and that nothing electrical is anywhere it can fall in. Filtration matters less if you drain after each use.
The three drawbacks
Shape first: a bath is made for reclining, so you lie shallow rather than sitting shoulder deep, which is the depth the protocols use. Then volume: more water than an upright tub means more ice or a bigger chiller. Then the household: the bath is out of action while it is cold, which decides it in most family homes.
When to move on
When you are buying ice more than twice a week, when the bath being cold is causing arguments, or when you want to be shoulder deep. An upright barrel or insulated tub uses far less water for a better position, and that is the upgrade most bathtub plungers make rather than buying a bathtub chiller.
Questions people ask about cold plunge bathtub
Can you cold plunge in a normal bath?
Yes, and it is the best way to test the habit. You lie shallow rather than sitting shoulder deep, which is the main compromise.
Do bathtub chillers exist?
Yes, circulating water out through hoses and back. Check it can cool your bath's volume in a reasonable time and keep every electrical part clear of the water.
What makes people upgrade?
Ice cost, the bath being unavailable, and wanting to sit shoulder deep. An upright tub fixes all three with less water.