Lot of debate as to what if anything it does, spend some time on google. Unless your experiencing swelling most trainers say to avoid it. Lot of recent studies show it creates more issues then it solves when people are using it for sore muscles.
I do something similar
I only take cold showers
Ive taken an ice bath ONCE
Took way to much time and way to much money to fill my tub up with ice
Just take a freezing cold shower for like 10 - 15 mins
When my tendons ache I spray cold water on them from the shower head. That feels great so I'd imagine an ice bath would be incredible as long as I could heat wrap my junk.