I did face plunges (as JKruse recommends) in increasingly cold water for a couple of weeks and started finishing showers with cool water....working down to the coldest setting - only briefly at first.
Then I started with baths, which were easier than showers, of 10 minutes in approx 60 degrees F water. I didn't have a suitable thermometer in the beginning so I'm sure of the exact temperature. I worked down to 50 F for 60 minutes over 5 - 6 months.( Pls feel free to message me if you want more specifics.)
I have to tell you my first attempts
were stressful....not the bath so much as the struggle to warm up after. Actually the baths were bad and the warm-ups horrendous (I suffered mild hypothermia). I don't recommend doing this without someone to check on you. I don't recommend risking hypothermia at all. I would also recommend using heat to help re-warm (before you adapt to where you heat yourself in response to cold on the skin) if that makes you comfortable.
Just to differentiate between cold stress and cold adaptation.....your body should
adapt after repeated cold exposure ("stress") on the skin. That's not to say everyone will of course! I personally experienced signs of adapting from 3 weeks after starting cold baths. My temperature began rising after I got in the cold water. (Later on, my temperature started rising in anticipation of a cold bath!)
After about 5 weeks my body temperature taken in the morning and early evening was normal (98 - 98.6) more often than not. Before, since early adolescence, my temperature was usually 95 - 96 degrees. I dreaded the onset of Winter and found it so hard to warm up.
I've been ice bathing for 2 1/2 years now. Though his year I stopped at the start of September - that's Spring here.
I'm solidly adapted to cold temperatures - or cool ones anyway. I haven't used any heating in the house (when I'm home alone) the past two years and I haven't worn a Winter coat in all that time either. (I do live in a
relatively temperate climate I guess? No snow here but we do get frosts.) I'm comfortable sleeping outside, and inside I use little bedding.
Improvements, apart from sleep, were with normalising body temperature, my spleen stopped being so swollen, and my fitness level increased to where I stopped feeling breathless climbing hills or stairs. I've been well enough to get out of the house 20 - 25 hours a week. I'm able to accompany my kids and be involved in their activities, and I do volunteer work. I still have ME, but I'm much better than I was a few years ago...and I'm much happier in Winter.
I'm planning to resume cold baths in Autumn....once or twice a week seems enough these days because I get cold stimulus (stressful before adaptation, not so afterwards) just from wearing less, using no heat etc.
^^ Hope that explains well enough.

Anne.