This presumes that the camera is in a fixed position following the skier. I use portrait mode while skiing behind or beside my subject. The larger image of the body and skis provides a clearer mechanism to identify ski performance and body movements.
One thing I would add if the budget allows (i.e. ski school or race club) is getting Coaches Eye. You can use your phone or tablet but the beauty is you can edit on the fly. Things like while playing back the video, you can control the speed back and forth, and you can draw line like you see (or at least used to) the commentators do in football games on TV. This enables you to show the person things like if their shoulders, hips are level, hand placement etc. Just add a line or circle where something should be in contrast to where they are.
I don't know what it costs but there is a free trial period and after that there is a license fee. The club pays for it but I don't think it is a lot, or at least once bought in as a team, additional licenses aren't as much.
For MA a camera with a long zoom is to be preferred for zooming in as the skier approaches. However, the most important thing is to keep the camera steady. The better you are at filming the better the video will be for MA. I use Vegas Movie Studio 15 Platinum for editing. Then I upload the material to YouTube. Ive done thousands of such video clips.