Slate's Explainer has an answer and question post about moonwalking. Here is one of the very good questions answered there.
Would it be easier to moonwalk on the moon?
The Explainer says "absolutely not" and attributes this to the awkwardness of walking on the moon. The article gives an example of Earthly legs being too powerful as the "astronaut's hop". The explainer also says it is awkward because of the pressurized space suits.
I think the problem is almost entirely the pressurized suits. I believe that the astronauts do their moon-hop because it is difficult to bend their legs in the pressurized suits rather than because the gravitational field is smaller.
Suppose you had a space base on the moon so that you could be on the moon and NOT wear a space suit. In this case, I think moonwalking would be essentially the same as on earth. As I showed on my previous post on moonwalk, the move has a lot to do with center of mass and the ratio of the normal forces on the two feet.
On the moon, the ratio of the two forces would still be the same as on Earth. I could be wrong. The only way to know for sure is to build a moon base so that we can test this out. Well, I guess someone could go up in the vomit comet while they are simulating moon gravity.