Ski bases do oxidize but the rate of oxidation of polyethylene is very, very slow. What is happening is that the sharp edges of snow crystals are shredding the polyethylene base where ski/snow friction is greatest, which means usually along the edges of skis.
Base burn is not burn per se resulting from heat (unless maybe you are a competitive downhill racer) but the ripping of polyethylene micro hairs from the base or "shredding" by the sharp spikes of snow crystals. At least at the speed most mere mortals ski. If the base contains graphite, some of the graphite also falls out further contributing to the grayish/whitish look.
If you were to sandpaper the ski base at the edge you would get approximately the same result. Although there is friction involved, it is abrasion and not heat or oxidation that is causing the edge damage.
Regardless, the best preventative solution is to wax well before you ski. On my SL skis I use Swix CH3 powder sprinkled along the skis edges over the wax of the day before I scrape and iron in. Depending on the type of snow and the speeds and turns you generate, you may not need to do it often. CH 4 crayoned in along the edges can also work.
Fresh snow has sharp snow crystal points. Man made snow is also quite abrasive. Older snow less so. Try skiing in the spring with shorts and taking a fall and you will find out how abrasive snow can be. Better yet look for other persons who have.
I could be wrong about this, but that is my understanding of the terms "oxidation" or "base burn" that are used to describe what is really an abrasion process that occurs along ski base edges. Once it has occurred and is quite visible, only a stone grind will "cure" the problem. Waxing will help prevent more damage and conceal existing damage but will not eliminate it, and your skis will be slower.
If the damage is slight, a good, sharp steel scraper may "shave" off the micro hairs. However, unless you are very good with tools, a steel scraper can cause a lot of more serious damage to the ski base.
: Whenever the scraper skips you will have a new horizontal scratch in your ski.