Walk-in tubs provide more stability during bathing than traditional bathtubs. Once inside, the bather can sit down in a preformed chair that is part of the tub.
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Caulking is a fix-all for all sorts of situations since it’s a great adhesive in a pinch, but it shines at filling gaps. You might even call it “weatherstripping in a tube.”
Phone apps are good for predicting a possible freeze, but nothing replaces verification that an actual freeze happened. Maximum/minimum thermometers are a good bench check against your phone app or the National Weather Service predictions.