Walking dogs when you don't actually have to is really stupid when you have chronic fatigue. However, it is a great way to get some fresh air and spend time with your family. Of course, the most important thing is to look awesome.
I recommend dragging yourself out of bed at the last minute, grabbing a pair of jeans and a t-shirt that are already dirty, chucking on a functioning coat, pulling on the first working hat you find and your most practical shoes. This saves time and energy and also gives you a great "I don't give a fuck" air.
You don't want clean clothes as there's usually mud, and dogs, and generally dirty things that will most likely find their way onto your clothes. If you wear clean clothes out this can mean extra washing, and so possibly spending more spoons. The t-shirt and coat combo keeps you warm but allows you to keep cool enough not to over-heat after walking for ten minutes if, like me, your body has no idea how to regulate temperature. The coat can also keep you more dry than a hoodie or jumper. The hat can keep your ears warm if need, keep come sky tears off your hair and hide your bedhead if you don't want it on display.
A pair of shoes that scream "PRACTICAL AND UGLY" is essential. These are particularly un-pretty, comfortable, waterproof, breathable and designed for walking. It shows you care about your feet and not about how you look - what's cooler than that?
Accessories are key with this look. A lead is a versatile piece of decoration which you can wear around your waist like a dog walking belt, or around your neck/shoulders like I have here, like a scarf.
Poo bags give you the serious dog walker look. You don't fuck around. You're real as they come.
A bottle of water is essential for staying hydrated. Apparently people with chronic fatigue need 12 glasses of H2O a day rather than the average person's RDA of 8. 

If you need an inhaler, keep it on you. Especially if your asthma is triggered by pollen and it's May. I recommend getting a whole load from your doctor and keeping one in every coat and bag or as many as you can at least, to keep the forgetfulness that comes with fatigue from giving you an asthma attack in the middle of nowhere. Also, if you spend a lot of time with someone, it's great if they can carry one for you, too.
The final and most important accessory for this ensemble is a dog. Dog walking without a dog is just walking, and carrying around the lead and poo bags without on will make you look like you've lost your dog are generally a massive tool. They also make your heart happy and want to make you feel better when your lack of spoons is getting in the way of your happiness. Dogs are great. But don't get one if you can't provide it with the life it requires, please.
Hat | Local Convenience Store
Coat | Primark
T-Shirt | Mate's Clean Washing Pile
Jeans | New Look
Shoes | Eco Vegan Shoes
Dog | Belongs to my dad, adopted from my step-brother.
! ADOPT DON'T SHOP!
I hope this has inspired you to keep style in mind in such a casual situation. Life is all about looking good, after all.
Peace.