First of all - unless you are very physically active, you don't need to bathe (or shower) every day, especially in winter. If I did, I'd be a "walking flake" as my skin is VERY dry normally, and worse in winter when the furnace is blasting and the air dry. So every other day...sometimes even every third day, unless I've been REAL busy (like cleaning house, or cleaning out closets, or doing several loads of laundry -- bending, sorting, folding, up and down stairs, carrying, etc.) We Americans tend to think daily showers...and even multiple showers a day..are a GOOD thing. That's really not necessary.
Thorough washing of underarms and nether regions daily, and of course the usual face/hands is sufficient. Clean socks and underwear help.
I have a small bathroom and apparently have gotten used to it being cold. I am in/out of the shower in 20 minutes, including shampoo (usually twice), swabbing down the walls with a sponge, drying the floor. During the summer I may shower every day, especially when it's hot -- a cool shower can cool me down pretty quick. But now that it's winter, it's more like every other day, or even longer.
There are small heaters you can put in the bathroom so you don't have to run the shower or tub for warmth. That might work for you.
...I am not a doctor, nor health professional, and don't pretend to be one, here.....