Chipper, my little Yorkie-Poo, absolutely hates any kind of mud and doesn't even want to get his little paws wet.
He also does not like having to take a bath; but he tolerates that; I think because it is at least warm water, and not cold.
We have some of those little cement stepping stones out in the front yard. It is just so cute watching Chipper hop from one stepping stone to the next one so that he can keep his feet from having to be in the dirt.
He usually hops on the walking stones even when the ground is dry, since he has seen me walking on them; but for sure when he has to go outside and it has been raining; he always uses them .
I think it really depends on each dog, whether they like water or not; and I have never ever seen any dog playing on the mud like the one in the picture is doing.