Question: When I ski with my gopro, I usually have to use the wide FOV because it's too difficult to carefully frame my shot while I'm skiing since I have to, you know, ski! I often am chasing some of my friends who may be right in front of me, or off to the side. The resulting footage is a little underwhelming since the subject is so small on-screeen. 

Since I can shoot this wide fov footage in 4k and only really need 1080p footage, I would like to have a moving crop at 1080p centered around the subject, preferably undistorting and stabilizing the image at the same time. Is there any video editing software that would allow me to do this?

Answer: 
Pretty much any modern NLE will allow you to do this, with varying levels of difficulty. For example, in Davinci Resolve you could do most of this in the free version, except for removing the fisheye effect which is I believe only available in the Studio version.
After Effects would be the go-to choice for doing this. You can use the "cc\_lens" effect that comes with AE to undistort footage - if you want to be very precise though, you can undistort using a fixed focal length, but that is only possible with third party plugins or more advanced compositing programs such as nuke or pfTrack (as far as I know). Scaling in on the footage shouldn't be a big problem when you first undistort the image. However, you might have some issues with chromatic abberation, especially when framing a subject close to the edge of the screen. Here's the pipeline I'd take for polishing such footage:

1. Undistort the footage using cc\_lens or something similar.
2. Stabilizing the footage by either camera-tracking the shot and transforming the Footage or by using the warp-stabilizer.
3. Zooming in on the area you want to focus on.
4. Reducing chromatic abberation, using methods like [this one.](https://www.youtube.com/watch?v=lOSxK45JksA)

The last step might be color correction, grading and adding some artificial camera shake, since you have probably stabilized the footage already. Quick, sudden shakes usually looks unpleasant, but slow moving shakes can look more organic and visually pleasing.
Hope this was helpful, have a good one :)