Is white/brown-out effect hazardous during the landing roll out?
From a partial accident list on Wikipedia, the issue seems to affect only helicopters.

A fixed wing rolling out should have no issue. As the dust/snow cloud will be behind the windshield. A plane landing in sequence should wait until the dust/snow settles.

Also an approach in poor visibility caused by a sandstorm would be no different than an approach in fog. An instrument approach will be carried out.