I did some calculations based on the this article referenced earlier.
The main concern appears to be the required power output.
To stay above the water, you need, roughly
$ m g=1/3\rho A v^2 $
where $A$ is the area of your foot step, $v$ is the speed of your foot kicking the water, $\rho$ is water density.
And the power output required is $p = m g v$.
The power output an animal is capable of is roughly proportional to its mass, so we want to look at the required $p/m$, which, from the above, is
$ p/m = g \sqrt{m g/(1/3\rho A)} \sim \sqrt{m/A} $
Now we see that the required power output needed per unit mass is roughly proportional to the square root of the size of the animal (assuming the shape is the same) The bigger you are, the harder it is to run on water. So, if a human can not do it, a moose will find it even harder.