For true vertigo (like positional vertigo, which I get once or twice a year), I've never found Antivert (meclizine) to do a bit of good. But I've always had that merry-go-round/funhouse feel when my head suddenly changes position, not really while I'm skiing. And yes, I will have that for six weeks stints during ski season. There's crazy maneuvers the doctor can run you through, but I haven't ever made an appointment to do it. I tried to do it myself once, made it worse.
But, skiing where I do, I regularly get conditions where a true vertical stance as you come to a stop is not quite clear for a second, or you think you've stopped but you haven't. And it takes a few seconds to get your equilibrium under control. I might stop and shake my head a bit because I'm losing my grip on what is up vs down. I wouldn't say I get nauseous exactly. The older I get the more flat light and fog affects me. I think maybe some kind of contrast vision is being lost as I age. So, yes, I have both true vertigo and frequently a skiing type of "vertigo" that is nowhere as bad, but still undermines your confidence. And I've taken several falls due to fog. Twice because I thought I was stopped when I wasn't. Twice because I couldn't see a radical anomaly in the snow surface and just slammed into it.
Certain goggle colors can help with contrast when it's a flat light problem. I use rose tinted ones. Then the rest is tactical. Don't select slopes without trees you can either ski alongside of or dive into. Even on a really foggy day one side of a run may have more "shadow" from those trees. Figure out where the sun is, then figure out where the slightly more shadowed side should be. Slopes with choppy conditions are easier to see than untouched powder. Yes, we all love first tracks, but if there's no trees and it's socked in, you need some texture to show you the slope. Second choice is slopes with other people (moving trees). Follow a friend, make them do the work. This is not a time to ski wide open bowls.
Now meclizine can help with vague nausea due to fog. But it won't help you ski it. Planning your route is what you need. Maybe see if there's a part of the resort below the fog layer. And, worst case, and something I've done, is to just swallow your pride and download.
