For mud, I always hard brush all the mud off first thing. If you think about it, the curry is just going to grind all that dirt in. After you get as much as you possibly can off with the hard brush, then go in with the curry since now it'll actually be able to do it's job kicking up the dirt and hair, then proceed to brush as you normally would.
And for shedding, I tend to be old school, just tons of currying with a regular rubber currycomb. It's great for skin and works to get all the hair out. A good rule of thumb is to curry for at least 10 minutes every day!
You can buy some of those expensive scrapers, but finding out that the rubber side of a sweat scrape does as good, if not better a job, was game changing during shedding season. I groom as normal to get most of the dirt, sand and dust off then give them a sweep over with the sweat scrape (make sure the horse and scrape are dry). It takes massive chunks of loose hair off.
We have on cob who has an awful winter coat, and when she sheds, she gets really itchy and waxy so we just keep her clipped all over.
As for mud, unless they're going somewhere, I just brush it off with a curry comb and dandy brush, making sure the saddle and bridle areas are clean but not that fussy about the rest as it can get very muddy in this country. Continuously washing legs and getting them muddy, then washing again causes more problems that it solves. It's best just to leave it dry and rub off the worst of it. The horses all get a good wash when it gets warmer.