The most common and most likely answer to this crossword clue is the 4 letter word MUSH
I've seen this crossword clue in Financial Times
M
U
S
H
Buddy explains!

The straight part
We know that "Cornmeal/said to get dogs moving" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cornmeal/said to get dogs moving = mush.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does MUSH mean?
MUSH noun- A somewhat liquid mess, often of food; a soft or semisolid substance.
- A mixture of noise produced by the harmonics of continuous-wave stations.
- The foam of a breaker.
- A magmatic body containing a significant proportion of crystals suspended in the liquid phase or melt.
- To squish so as to break into smaller pieces or to combine with something else.
- A food comprising cracked or rolled grains cooked in water or milk; porridge.
- Cornmeal cooked in water and served as a porridge or as a thick sidedish like grits or mashed potatoes.
- A walk, especially across the snow with dogs.
- To walk, especially across the snow with dogs.
- To drive dogs, usually pulling a sled, across the snow.
- A directive given (usually to dogs or a horse) to start moving, or to move faster.
- A magic mushroom.
- (chiefly Southern England) A form of address to a man.
- The face.
- To notch, cut, or indent (cloth, etc.) with a stamp.