>I noticed that the Matterhorn is usually hit by clouds and strong winds right by the peak. With that amount of windshear it gets every single day, how does it survive?
Generally, the intrinsic strength of most rock is going to be way higher than any sort of stress that winds on Earth could impart, especially if we're thinking about the stress necessary to induce large-scale failure of something as large as the Matterhorn. Similarly, outside of very specific environments, weathering and/or erosion by wind and wind blown particles is such a non-factor in the overall budget it's completely ignored (and it's basically only relevant/considered in hyper-arid regions where weathering and/or erosion that is mediated/caused by water or ice is minimal).
>How does it maintain that iconic peak?
We can start with how it generally got its iconic form in the first place, and where it was shaped by surrounding glacial erosion, effectively being the head of four different glacial cirques. The ability to for high, steep slopes/cliffs like those in the Matterhorn mostly comes down to the intrinsic rock strength of the composing material and where the strength of material in this case can be considered through a similar lens as we would think about the stress necessary to fracture intact rock, e.g., Mohr-Coulomb theory. In this sense, intrinsic material properties (that we quantify through things like the cohesion and internal friction angle) are going to set theoretical limits for how large a "tower" or cliff one could be sustained (e.g., Barton & Shen, 2018). Generally (and first thinking about relatively isotropic rocks), more crystalline rocks (like the gneiss that makes up much of the Matterhorn) will have higher cohesion and/or internal friction angles, meaning that generally they can maintain steeper / higher cliffs before failure through fracture formation. This becomes even more true when we consider that crystalline rocks tend (on average) to be more isotropic in the first place and where rocks with lots of "planes of weakness", i.e., planar heterogeneities like bedding planes or existing fracture planes that have lower cohesion and/or internal friction angles than the rest of the rocks, tend to be more prone to failure, especially in the case where those planes of weaknesses are favorably oriented with respect to the applied stresses for failure (e.g., Cruden, 2003). The presence and orientations of fractures and other planes of weakness in a rock mass will reflect its geologic history, e.g., is it a sedimentary rock that was deposited in such a way to favor lots of well developed bedding planes vs a more "massive" deposit, how much tectonic deformation has it experienced in the upper crust to form various fractures, etc.? This geologic history in turn effectively sets limits on how "strong", at a large rock mass scale, this material will be and thus how large / tall / steep a feature it could support (see again Barton & Shen, 2018 for a run down of some of the math behind this).
>I was imagining just from the last 100 years alone the shape of the peak should have already changed, like it would plateau or something.
So 100 years is effectively no time geologically speaking, but even with the considerations above, things like the Matterhorn are pretty ephemeral geologically speaking. While wind is effectively a non-factor, plenty of other weathering processes do act on parts of the Matterhorn and similar features. For example, frost-cracking (or frost-wedging, freeze-thaw weathering, frost weathering, etc.) can be an effective weathering mechanism for breaking down portions of expo