homestarI would be interested in hearing more about this. I've always edited ski videos using the songs as a sort of template to fit the videos into.
Editing is a very musical art form. You are arranging aural and visual elements creatively. Notice how I didn't say "syncing" or "matching."
When a band plays a song, not everyone is hitting notes in perfect unison. Imagine if a song had each drum hit and note play at exactly the same time with nothing in between. Pretty boring and staggering, right? The way music works is that each part both stands on its own and is harmonious with the others. A drum beat has fills and textures between each hit on "the beat" (which is the "cue" of the beat that the other instruments aim to align with). A bass guitar will hit the root note at the same time the drummer hits the beat, and in between those hits the bass and drums might go in different directions (fills). These different directions sound musically pleasing as long as they reunite on the beat. My point is that each instrument weaves in and out of alignment, and the points in the song when they align are decided consciously and artistically. In between those moments of alignment are harmonious but contrasting "fills" that operate on some shared fundamental level (tempo, time signature, key) yet still go off and do their own thing. There are intentional sections where they are not aligned because by definition the alignments only exist in contrast to the parts that are not aligned. It is a dance, not a march.
Your shots are made up of "cues" - visual signifiers that catch the viewer's attention. This could be the skier absorbing the landing, doing a pow slash, or a lens flare. This also plays into the concept of gesture: the defining geometric and spatial character of the object. The gesture of a bullet is not a pill-shaped object, but a straight line. These cues are the most fundamental element of what you're portraying visually. Think of them as notes, or chords.
Think of your timeline as a band on stage. Each visual cue will have its own propensity and cadence, as will many parts of the music underlying it. Your job (and this is totally an opinion on my part - there is no "correct" way to make art) is to arrange these elements in a musical way rather than mindlessly aligning them. So yes, you have the right idea in that you will want to sync visual cues (e.g. cuts, landings) to the beat of the song, but you want to do this strategically and with the overarching flow the video in mind. You want to build up to it then "unleash" it at its climax. You want to create moments of tension, contrast, and resolution in the way you align elements in your edit. If everything is emphasized, nothing is emphasized.
I can't find a particular example, but look towards the end of this video when things speed up. Yes I am syncing cuts to the beat (but not excessively), but I am also looking for gestures in the shots that "bloom" in a way that compliments (not matches) the cadence of the song and the overall "feel" of the edit. For example, the snow spray dispersing all over the frame in unison with the drummers crash cymbal fills at 2:12, or the ending shot of the skier falling out of view as the song concludes and "departs" with you.
tl;dr be mindful of tension and resolution in how you arrange things on the timeline. Gesture and cadence are king.