MirrorFinishMan gave as good advice as you’ll get, using the yellow dishwashing gloves and some thin cotton-glove inserts is the way to go. My only other advice is to add a quart to a gallon of hot water to the wash bucket (how you go about this is up to your creativity). THIS IS NOT ACCEPTABLE BELOW 35 DEGREES – at that temp, you shouldn’t wash the car. Your objective is to raise the water temp 5 to 10 degrees. You’ll be able to work with bare hands (my choice), and or just the yellow dishwashing gloves without inserts.
Sounding repetitive ... layer, layer, layer your clothes. It’s so easy to regulate your body temp by removing/adding one thin layer at a time than to try and do it with a bulky jacket/coat. Preventing the hands & feet from getting cold is priority, getting them wet will increase how quickly they get cold. Once they’re cold, the rest of you will feel cold too. Gloves and good thick socks in waterproof boots are key. My added recommendation on the waterproof boots is to get a true rubber sole, or one of the light-colored soles. Depending on the solvents you’re using to clean the wheels, you may soften the cheaper, plasticized boot soles and leave black marks on light colored carpets as you get in and out of cars.
At any age, it seems you’re doing what you like and making money doing it. You’re to be congratulated – most kids today don’t have motivation to clean up their rooms let alone the work ethic you do. Tell that to your Dad this when he brings up the utility bill again ... you may give him the perspective of what else you might be doing if he stifles your ambition and that may make him think twice. Or, detail his car(s) once a month as payment in full, after all, that’s worth a lot more than the money he’d get in return. Either way – I congratulate you on effort, ambition and determination.