I'm sure the OP has long since selected a camera and is happily getting great pictures of his son skiing, assuming he bought a camera that works well for that sort of thing.
Many of the comments that have appeared so far are correct, but may or may not be useful, since the basis for some of the statements regarding what's best are not explained very well. The OP hasn't asked any additional questions.
With that said, I can't resist offering a few comments of my own.
As with ski racing itself, for a camera to photograph ski racing, speed is a Big Deal.
That speed comes in several different flavors. For example:
How fast/well does the autofocus work?
What is the maximum continuous shooting speed?
How is the image quality at higher ISOs?
What is the maximum aperture of the lens being used?
Of these four questions, the autofocus (AF) is perhaps the most difficult to quantify and understand. There are multiple factors contributing to the effectiveness of the AF for shooting things that move. These include how quickly the camera acquires focus, how accurate that focus is and how accurately it is able to maintain focus on something that's moving.
Now, you might think this depends on the camera body you're using, and you would mostly be correct. But not entirely. For every camera brand on the market, there are some lenses that focus much more quickly and accurately than others by the same company. Just to make things more complicated, not all expensive lenses are the best for focusing on moving subjects. In general, though, when telephoto lenses are involved, more expensive lenses with larger maximum apertures will focus faster and maintain focus better. There are some reasonably priced lenses that work well, too, but it can be difficult to find out which "amateur" lenses focus quickly and which do not.
For bodies, finding out AF capabilities is a bit more straightforward. Many testing sites (DPReview comes to mind) devote some energy to testing how well cameras focus on moving subjects. It pays to read some of these reviews carefully. In general, even today, the traditional DSLR configuration with the flapping mirror still reigns supreme for action photography. This is because DSLRs have a mature version of what is known as Phase Detect Auto Focus (PDAF). For several reasons, PDAF works better for action than the method that is used on so-called mirrorless cameras (whether or not they have interchangeable lenses). That method is known as Contrast Detect AF (CDAF). Some mirrorless cameras have implemented PDAF or hybrid PDAF/CDAF systems for the sole reason of improving focusing capabilities on moving subjects, but they still don't work as well as the best systems on DSLRs. Some of the mirrorless systems work pretty well, though, and they will surely get better. It should also be noted that PDAF is extremely complex and prone to mis-calibration. For static subjects, CDAF is often more accurate.
Just to clear here, not all DLSRs are created equal, and some are much better for action work than others. Among current DSLRs, the full-frame cameras ($$$$) are generally pretty good, and the top-end APS-C cameras (Canon 7D II or 70D, Nikon D7200) are excellent for being able to achieve and maintain focus on moving subjects. Entry-level DSLRs of any brand have their strengths (very good image quality), but they have less sophisticated AF systems. For most hobbyists, the APS-C cameras make a lot more sense than the full-frame cameras, and the effective "reach" with any given telephoto lens is about 50% greater than with a full-frame, which is another characteristic useful for sports and wildlife.
Among the top APS-C bodies, Canon has a few more focus points and many more cross-focus points than Nikon, and so arguably has the better focusing system for action. However, DPReview seems to believe that Nikon has better algorithms for following action and achieves a better "hit rate" of in-focus images. The Pentax K3, while a dream camera in many ways, seems to have a focusing system that is not as well developed as the Canon and Nikon systems, although a pretty good success rate is still possible.
I should also point out that these comments regarding AF only apply when using the eye-level optical viewfinder that all DSLRs have. Using the LCD on any DSLR may be preferable for macro and tripod work, but it's completely useless for action. If you like to take pictures using the LCD and holding your camera out at arm's length, a DSLR is a poor choice for you.
And now, just for fun, a couple of photos of moving subjects (albeit no ski racers) done with an amateur Nikon that is now two generations old having an AF system that received many complaints on the internet. These were done with an amateur grade 70-300 zoom lens - but not with Nikon's significantly slower-to-focus, and cheaper, 55-300 zoom lens.
Subject moving directly toward camera. This demands that the lens be able to re-focus quickly.
This was clear day with good light. The subject was smaller, but moving in a predictable fashion. The image is quite sharp when enlarged.
Anyway, a bunch of rubbish that may not be of any real interest to anyone. I hope someone finds it at least marginally useful.
Edited by jhcooley - 4/22/15 at 4:46pm