I haven't checked the temp on our water, but it is winter and I assume it is at least a bit colder than summer, or at least it feels like it to me. Before I first go under I take a breath in and as I go under I let the breath go in a long relaxed exhale. It seems to make it bearable. After I am in, I'm good for the duration of the shower. Days I shave it is from start to finish, somewhere in the 7 to 10 minute range I estimate. Days I don't shave I start with warmer water and then as I start to rinse off soap I go full cold, probably 3- 5 minutes. I have music playing when showering so have a rough idea of how long I am in the shower.
Towards the end I let it run on top of my head until I start to feel that wonderful ice cream headache and then I go to the back of my neck. After a bit on the back of my neck it sometimes puts me into the same mode I feel meditating. I have no idea why that is, but it is a good feeling.
If I can get someone from the family to come along I will take the polar plunge into Lake Michigan on New Years day. After about 30 seconds I can't fell anything from about my shins down and it feels like walking on stumps.
The worst year for that was in the college days home from break during a brutal Midwest winter. You had to go in off ice cliffs and there were people with ropes to help you climb out.