This question became of acute importance to me a few weeks ago, after some bicycle-related lithobraking. The answer turns out to be fascinating.
Water is quite an odd substance. In terms of phases, we have three phases we’re familiar with: gas, liquid and solid.
However, what we know as ice is not the only possible structure. In total, there are eighteen different crystalline phases, with several more theorized to exist, and a few amorphous ones as well.
The regular ice we see on Earth is of type Iₕ. At a pressure of 2099 bars and -22 °C, it transforms into Ice III, then into a series of others.
All of these have radically different crystal structures, from hexagonal with Iₕ, tetragonal with III, then monoclinic (look it up) with V, tetragonal again with VI, cubic with VII and so on.
As an aside — the only other compound I know which is even close to being as weird as water is plutonium.
If you look at the bottom of the graph, at ambient pressure, the stuff passes through a whopping six phases before melting at 639 °C.
What’s worse, is that all of these phases have vastly different volumes — in total, from α to ϵ, it changes 25.4%.
Imagine having to cast a sphere of the stuff in an extremely particular shape, then store it for a prolonged period of time, even though it has some internal heat production due to radioactive decay, then having to predict the way it behaves as it heats up in microseconds — quite a challenge.
To return to the original topic, note that the line between Iₕ and liquid water curves away from 0 °C slightly. That would suggest that with sufficient pressure, water would turn liquid again, explaining the slipperiness.
It was quite difficult finding quantitative information on this, but in the end, I found a series of papers on solid-liquid equilibria. These turn out to be described using so-called Simon-Glatzel correlations:
Here, p₀ and T₀ are reference temperatures, for which we can use the triple points of the respective phases. Plotting this between 0 °C and the triple point of Iₕ, III and liquid water gives:
It’s immediately obvious that this is completely insufficient. At even a moderate temperature of -10 °C, you’d need to exert a pressure of 1112.6 bars to get the ice to melt. Considering people can ice skate at temperature of -20 °C and below, requiring an obscene 1953 bars, this can’t possibly be the only explanation on why ice is slippery.
A different explanation focuses on friction. Friction between an ice skate and the ice itself would result in energy being released, which would subsequently melt some small layer, enough to result in a slippery surface. This works fine for a moving skater, but it contradicts the experience that ice is slippery even when moving slowly.
As with the previous explanation, there is some range where this is a viable explanation, but it’s not universally accurate.
A much more interesting perspective is granted through molecular dynamics. At the edge of the solid phase, there is inherently some disorder. Ice tries to orient itself with hydrogen bonds, but on the edge, those aren’t available.
By simulating the resulting system with molecular dynamics, it turns out there is a thin layer of dangling -OH bonds at the ice surface, resulting in rotational motion of the uppermost water molecules, distorting the ice lattice.
This then causes a slight surface melting of the ice crystal and a low friction coefficient.
All of this goes to show just how fascinating even the most ordinary of events can be. It’s the beauty of physics: using phase diagrams and molecular dynamics to explain faceplanting in a frozen car park.
 David A. Young. Phase Diagram of the Elements. Lawrence Livermore National Laboratory, 1975
 D.L. Clark et al., Plutonium and Plutonium Compounds, Los Alamos National Laboratory
 Mathieu Choukroun and Olivier Grasset. Thermodynamic model for water and high-pressure ices up to 2.2 GPa and down to the metastable domain. The Journal of Chemical Physics, 127(12):124506, 2007
 T. Ikeda-Fukazawa, and K. Kawamura. Molecular-dynamics studies of surface of ice Ih. The Journal of Chemical Physics, 120(3), 1395–1401, 2004