A Mudi does not require daily coat care or maintenance. A comb through will do the job perfectly, I stress the Mudi should not be bathed too often otherwise it will make the curly coat appear fuzzy.
Bathing the Mudi
When I am bathing a Mudi, my shampoo of choice is one specially designed to deeply cleanse the coat, my dogs spend their days running through grass, mud, and water, even though their coats clean themselves it would surprise most how much extra dirt a good shampoo will bring out of a coat! If the Mudi is black I will bath them in a enriching shampoo especially designed for Black/Dark dogs to make the coat stand out at its best, similarly if I was to bath a true white Mudi I would likely use whitening shampoo to add an extra touch. No matter the mudi or colour, I rarely use any conditioner. I do not want the coat becoming any softer than what the shampoo will already make it.
When it comes to drying, a Mudi should never be dried with a blaster as this will make the coat go straight and out of standard. At most a quick towel dry before letting the coat dry naturally is best. If it is particularly cold, or your mudi coat is not of the type to dry quickly, cage drying on a low setting is the next closest option to keep the coat in its natural state, my mudi spend a lot of time swimming and diving into water, their coats are always dry in under an hour. It is a breed created to be weather resistant, they should therefore not struggle to be self-drying.
A place of difference I often see is the curliness or waviness of a Mudi coat; how curly it should be and how much it ranges from each dog, even in the same litter many of the puppies will have different levels of coat as adults, but this is no different to other breeds. I received a lot of compliments to Red's tightly curled coat even when she was younger, and yes, it is very much down to genetics on how much curl your Mudi's hair will have. However, a good trick if you want tighter looking curls is to keep a spray bottle full of water nearby and spray the dog all over a few times a day. It is not possible to do it too many times, after a few days you will begin to notice the curly hair to tighten up, forming tidy curls which stand out. The same trick will work to make a wavy coat stand out.
Below is a copy of the FCI standard regarding the Mudi coat;
Hair: Head and front of limbs are covered by short, straight and smooth hair. On other parts of the body, the coat is uniformly very wavy or slightly curled. It is dense and always shiny, about 3 to 7 cm long. At some spots, cow-licks and ridges are formed. The coat is longest on the back of the forearms and the upper thighs, where it forms pronounced featherings.