As an ex-trainer, I always get a chuckle out of this recent addition to mainstream training regimens. I saw it surface in NYC and LA about ... God has it been 15 years now? (ugh) It surfaced, then disappeared, but it's making a comeback.
It's naturopathy gone awry; good for little more than a shock to the system. Consult a physician before doing this, especially if you have any pre-existing medical conditions (diabetes, cardiovascular disease, weakened immune system).
Some trainers will tell you it's a great way to help increase endocrine and circulatory system strength, among others, but it's really nothing more than a way to take up time - easily taking 10 minutes out of the typical 1-hour personal training session. In other words, some trainers will actually have you do this in the middle of your workout routine, while others will consider it part of your workout, cutting your workout short by up to 10 minutes.
The last time I checked, this wasn't part of the training provided by the American Council on Exercise. It has become common for rags like Men's Health to do write-ups on naturopathic "medicine," so there's no doubt most trainers are getting into it based solely on what they're reading straight off the magazine racks.
In reality, it works only if you believe it does. If you use a trainer, and your trainer breaks up your workout by making you jump in the shower, you're obviously wasting your money. I'd tell that trainer to drop the subject and keep me on the floor. I'm not paying him to take a shower (unless he wants to shower with me). If he tells you to do this after your workout, don't bother. He doesn't know what he's talking about.
Contrast showers ARE great when performing yoga, or doing some extended stretching routines ... something best done in the privacy of your own home, on your own time.