For a long time I've noticed that after the end of a ski (particularly on hard snow) that the glide areas of my skis will turn whitish. Here's a nice answer from SkiPost that addresses the issue and gives a nice easy test to see if it's a base issue or no. (Hint: the answer is to brush out the ski and see if it goes away).
White Marks on Bases?
I skied 42k classic race today in firm tracks. Skis were white 8" before & 8" behind kick zone. WM
You ride a classic skis flat over a longer time than a skate ski so the glide zones will magnify any issues even more than skate skis will. Classic skis often have shorter higher pressure glide zones just ahead and just behind (especially behind) the kick zones which again magnifies any issues. These higher pressure zones with long flat contact times can cause a ski to "get white" if you have a sealed base, or even if you had excess wax in the base and did not brush enough.
If you did not brush your skis out enough with cold hard wax the white may be excess waxed pushed out of the base during the ski. If you brush it slightly and the white disappears it was likely due to excess wax remaining in the base. Next time on cold days brush inside and then after a warm up in the cold snow brush again to remove any wax that was pushed out during the contraction of the bases when it got cold.
If the white remains after a slight brushing then it is likely base damage. If the base is in fresh open condition you would see little whitening, but if the base is sealed slightly or more your bases will dry out quickly especially in cold fresh snow.
I suggest you get some base work done on your skis. Either a complete stone-grinding to bring up fresh base material. Or get a coarse steel brush and brush the heck out of the base, then fibertex coarse... What you want to do is remove the very outermost base material to expose fresh base material. Then start with a soft wax like Start SG2 and soak the base then SG4 and then proceed to colder harder waxes....
Andy at SkiPost/Start