Oh, you just load those as they are.
Though, first, it depends what tileset you're using.
However, most tilesets have black as the "transparent color." What that means is, the first color in any CSet is automatically transparent - no matter what color it may be. Some people like to use purple or cyan for their transparent color if they want layerable tiles with a solid black color on them, as you can see in this pack.
For reference, if you open the tile page and double click a tile to edit it, on the palette in the bottom right corner, you'll see the color in the upper left has a x on it to show that it's the transparent color. No matter what this color is, it will never be drawn on a layer.
The main issue will be importing those tiles in the correct color. Some palettes or CSets won't have the whitish-blue colors of the tiles you're looking at. So if you're importing these into the default classic tileset, then use CSet 11 for the snow, and CSet 7 for the rain. If you're using another tileset, you'll have to find the CSet with matching colors.
I prefer loading things like that into one of the main CSets (0 / 1 / 7 / 8 / 10 / 11), because it will be consistent across the game no matter what level palette I use. But if you need to load them into a level-specific palette using CSets 2, 3 or 4, then you'll have to check each level palette and CSet to see if they have what you want. In a well-organized tileset, you should be able to switch between different palettes without having to recolor anything - but not every tileset is well-organized. Further, some tilesets are limited in color, while others use many. In standard classic, you'll want to use CSet 7 and 11 like I suggested, but in a deluxe set like Dance of Remembrance, you'll want to use level-specific CSets.
And once you get that set up, just draw them on layer-whatever (use 6, or possibly 5 for those kind of weather overlays), and whatever your transparent color is (typically black) will disappear once they're layered on the main screen.