Dog walker here OP. Muddy dogs are a big part of my life for several months of the year.
You said you'd hoped someone might tell you it gets better as they grow up
. There's a decent chance that it will get a bit better once they slow down a bit, but I can't promise anything!
Equafleeces are a godsend- the under belly and front leg (plus back leg if you get the full version) protection is just brilliant. They are expensive though, so it is worth looking for second hand ones or considering similar cheaper brands- just make sure they fit and offer the same coverage.
Different dog coats (as in their natural coat) deal with mud, water, being washed and dried differently. For example, mud seems to evaporate from beagles, washes off labs and springers relatively easily and is hell to rinse out of many of the gorgeous poodle crosses. So, much depends on the type of natural coat that your dog has and whether they are groomed short or not.
Similarly different dogs feel the cold a lot more than others depending on their coat, health, size and weight. Some can tolerate cold water well, others will find it genuinely unpleasant so don't let anyone tell you that dogs should easily tolerate being washed in cold water.
I've used lots of dog washers and have gone back to a pump action hozelock as suggested by other posters. I fill it with hot water and a little drop of gentle dog shampoo before I leave. I wrap it in an old blanket and it is usually nice and warm when I need it.
Dogs are rinsed off at the end of the walk. I then get the worst of the wet off with an aquasorb towel. These are bloody amazing, I can't recommend them enough. They are pricey but worth every penny. I have two and use them for loads of dogs each day- I just wring them out as I go along. Hopefully this link will work: amzn.eu/d/9aNSUGn.
Then they go into my van with loads of old towels. The best towels are old and crispy and just suck out the residual moisture.
Another useful thing is a mitt style washcloth for wiping or drying muddy paws. They are easier to wrangle with than a large towel, and take up less room in the washing machine.
If your dog dislikes being washed or dried it is well worth working to slowly and gently help them feel more comfortable. The best way to do this depends on how uncomfortable they are but googling force free, reward based desensitising methods should give some good suggestions. I've had great success with a lucky matt as a distraction which quickly leads to the dog no longer having an issue with being rinsed or dried.
Finally at this time of year I try to pick walks that aren't horrendously muddy. Or that have plenty of long grass or puddles towards the end which offer a bit of a foot clean and rinse.
Hope that helps a bit OP. Warmer times are coming and then the mud will ease off a lot until the end of the year.