While growing up I had to turn on the heater before taking a shower and sometimes when its getting late, you really don't have time to do that. Here's some advice which might help.
I'm going to go ahead and assume that any hot water source is unavailable and you are in a frame of mind where the water is too cold!!!
Step 1 - Making Peace with the Cold Water
Okay so you don't like cold water, the best way to make peace with it is to convince yourself that it's not too cold.
It's like entering a cold swimming pool, if you dip your feet in it for a while, it'll be easier for you to get in.
When you wake up in the morning, your body temperature feels lower because you haven't had breakfast yet, that's a good thing because it makes it easier to ease into the seemingly freakish cold water.
If you happen to have a shower, then turn the shower on and let it gradually touch your feet first, followed by your hands. Keep the water running and slowly ease in from the extremities of your body all the way to your face. You face is the part which you'll dread the most, so save it till the end after you feel like the body temperature going down.
If you happen to have a jug and a bucket of water, follow the swimming pool strategy. Fill in the bucket halfway and dip your feet and hands in it. Then slowly start pouring down the cold water on your hands and proceed.
One additional thing which might help is to have a towel on you. A towel which you could dip in the water and squeeze out/rub on your body will help.
Step 2 - Taking the Leap of Faith
You have to remember, practice makes a man perfect! Doing it the first time is much harder than doing it the Nth time.
After cooling down your body for a few minutes, hold your breath and step into the shower, as soon as you get into it, don't chicken out! The leap is the hardest, after it, it gets exponentially easier.
Same goes with a bucket of water and jug, when you're ready, repeatedly take a lot of water from the bucket and pour it over yourself. You start doing it, don't stop!
Water in which you were dipping your hands or feet it will actually be warmer and make it a bit easier, which is why I feel using a bucket and jug is easier with cold water.
Step 3 - Finish as soon as possible
Remember, once you get into it, there's no coming back, there's no point doing the whole procedure from scratch again. So, keep pouring that cold water over you, it gets much easier when you keep doing it. Pause for short breaks only when you need to use soap or shampoo.
Wash your body in little sections, torso at once, feet at once, hands at once etc. After you're done, get a fresh towel and hug yourself tight with it.
I've done the exact procedure I mentioned a several hundred times in my life quite comfortably, of course I like my hot water, but where there's a will, there's a way.