A better word would be splattered. His boots were splattered with mud. Sprinkled is better used with little candies on an ice cream cone or sprinkling glitter on a piece of paper.

Yes, the rainbow 🌈 colored things that you put on ice cream 🍨 are called "sprinkles". So things like that (or salt, pepper, powdered sugar ) which are solid are normally what you say are sprinkled. Splashed with mud would be more common.

Splashed would be the most natural word to use. You can sprinkle salt or sand - as Rosco said, the particles would be very small. You can't really sprinkle mud.

Yes you could use "sprinkled" here. But it would be saying there is only a very small amount of mud on the boot. It brings to mind for me very small particles of mud.

The sentence is correct grammatically. :) But, a native speaker would be more likely to say "splashed" or "splattered". We typically use the verb "sprinkle" either to talk about spreading something small with our fingers, or to describe very light rainfall. For Example: I sprinkled powdered sugar on the donuts. It [the rain] is just sprinkling.