Any cross section of your wall is supporting the weight of all the wall above it. In a first approximation, every cross section will be in a state of pure axial compression. The most heavily solicited cross section will be the one at the very bottom, which will be supporting a compressive pressure of $\rho h g$, where $\rho$ is the density of the ice, $h$ the height of the wall, and $g$ the acceleration of gravity. You could compare that value to the compressive strength of ice, and use that to determine whether your wall will crumble or not.
Your biggest problem would be to figure out what parameters to use, which apparently are very dependent on how the ice has been formed, what temperature it is in... Just taking a look at the phase diagram of ice, makes it clear that its going to have a complex behavior. It could be turn out that the compression force causes a phase transition of the ice at the bottom of the wall, so that you will then have to consider the top and the bottom sections separately. I have found a couple of very old references, here and here, which I have only skimmed diagonally. But that it is possible to write close to a 100 pages on the mechanical properties of ice kind of tells the story...
As an aside note, if you are willing to sacrifice perfectly vertical walls, having a wall with width growing as $A e^{by}$, where $y$ is vertical distance from the top of the wall, will have every cross section of it standing the exact same compressive pressure. This means that you are using all of our ice to its maximum load bearing capacity, plus avoiding different pressures creating sections with different phases.
