Well, nothing scientific than I'm aware of, strictly speaking, but I love the effect.

Right after the shower, you'll get super warm, even in winter. You're system just gets going to equalise your temperature.

Also, you'll be woken up no dithering about in a stupor until your coffee kicks in, it definitely gives you a kick in the backside to get going, so even just for that, it's worth it in my opinion.

And, I never get cold. I can work outside in a t-shirt in winter (UK winter) without feeling any cold.

A physiotherapist suggested it to me and did it himself, and I think the claimed benefit was our modern demon "inflammation". I'm not qualified to judge but it would probably help for people with some kinds of joint/back pain.

Edit: Forgot I also heard about it promoting an energetic response in the body (starting your engine for heat) to wake up for the day ahead and start burning fat before your first meal. I heard Tony Robbins talk about an ice room or something similar in his house that he uses for that. Probably not ideal for night time showers.