How do I get my spouse to take better care of his hygiene needs?

As a side note to the feeling cold issues. My husband got me a pair of electric socks. I'd always thought stuff like this was silly. Not anymore. They are great. My feet generally don't warm up until May (always been like that), and those socks make all the difference-helps me so much to feel warm all over. Perhaps that may help your spouse. Or a hot water bottle for his feet-I will use one for bed time, put it in about an hour before, feels great too.

I, personally, have a comfortable shower chair with arms and secure legs.
My husband has neuropathy and is afraid of slipping and falling in the shower.
So, after I take my shower, I tell him it's his turn. He uses my chair and the shower mat I bought for him that he can feel with his feet. So, he can stand when he needs and sit, too. And, of course, all necessary installed handrails.
Another thing he now uses because he can get cleaner, is a handheld attachment for when he is sitting.
First I bought him a non-slip mat that he could feel on his feet and now he is also using my shower chair. This pretty much resolved the shower issue for him and me.

Dee1956, when it comes to baths/showers for someone who is older, it is like going to the gym for a work out. Even I find it very tiring and I am in my 70’s. 

Some seniors become claustrophobic when in a shower. Especially if there are glass doors. Keeping the far shower door opened a bit could help. Sitting in the tub works but it is a major chore getting in to sit down, and more so trying to get up :P

Then there is the fear of falling. If your love one is using a moisturizing liquid soap and/or hair conditioners, it will make the floor of the tub/shower feel like an ice rink, even with a tub mat inside. 

Don’t get me started on towel drying, it’s an accident waiting to happen. 

A person doesn't need to shower daily..... twice a week or once a week is good enough, unless they are doing hard labor. Baby wipes work quite well between showers. Recently I found a product called “Water Wipes” in the baby section, quite pleased with the product.

I think you have to approach your spouse as if he's suffering from dementia brought on by the head trauma. As such, he needs to be treated and approached from a different angle if you want him to cooperate with you about taking showers. Fighting with him is not the answer. Your body language has to be kind and jovial, rather than confrontational, at all times. There could be other reasons you are unaware of that your spouse is either frightened of showering, or reluctant to get into the shower to begin with. For example, a gentleman who needed to help his wife bathe as she was no longer able to do so herself, was puzzled because she was calm and cooperative until he helped her step out of the bathtub, and then she became agitated and wanted to get covered up immediately. As it turned out, as soon as she saw her own reflection in the mirror, she thought there was another person in the bathroom, and she was embarrassed. As you can see, the cause of the distress for a person with dementia is not always readily apparent to the rest of us, who can take intact thought and reasoning for granted.

"If a person with Alzheimer disease is looking at a solid black area, or a solid white area, such as a bathtub, they may perceive a yawning bottomless hole. Putting a coloured bath mat down may increase the likelihood that they would be willing to step into the tub. Putting blue food colouring into the water may allow them to see what they are stepping into as well. Generally, with altered depth perception, it becomes challenging to judge how high, deep, long, wide, near or far things are.

If you send clear signals through your tone of voice, facial expression and relaxed and confident attitude, that you mean them no harm, they may trust you to the point where you are able to help them with their personal care. People with Alzheimer disease become extremely sensitive to the body language of others, as they no longer possess the judgment and insight to understand the situation, so they evaluate the threat posed to themselves by the frown or aggressive stance of the other. It is important to exaggerate your body language communication to let the person know that you intend them no harm. A smile on your face, a relaxed tone of voice and body stance, a sense of calmness and reassurance, perhaps a hug, all communicate that you mean to help, not harm. If you feel like you’re overdoing the positive body language, you are communicating your intent effectively for a person with Alzheimer disease."

This quote comes from "Understanding the Dementia Experience" by Jennifer Ghent-Fuller, a 33 page booklet which is extremely informative and available as a free download here:

Understanding the Dementia Experience, by Jennifer Ghent-Fuller 
https://www.smashwords.com/books/view/210580

Your spouse is obviously cold, which is another huge factor to not wanting to bathe. Have you made the bathroom sufficiently warm enough for him to feel comfortable? You can also consider hiring someone to come in to the house to help him with a shower once a week (which is sufficient); large wet wipes are good for interim wash-up's. Here is a list of 11 tips to help with bathing:

https://teepasnow.com/blog/11-tips-for-bathing-a-person-living-with-dementia/

Again, even if your spouse is not suffering from Alzheimer's/dementia per se, his actions mimic those who are, so the tips you're getting are relevant.

Watch Teepa Snow videos on YouTube as well; Dementia care pioneer Teepa Snow developed the hand-under-hand technique, as a guiding and assisting technique that provides family members and caregivers with an amazing connection. It promotes a physical touch connection that is friendly, comforting and attention-getting without being intrusive or overbearing. If you Google 'Teepa Snow hand under hand bathing' you'll get some video's and tutorials that come up.

Wishing you the best of luck with an issue that affects many people in your situation.