Good question! But before I answer it, your question sounds a bit more natural like this: "Can I use both of these?"
#2 is correct.
#1 should be "School is canceled tomorrow due to bad weather."
The reason that "schools are canceled" sounds wrong is because "schools" (plural, schoolS) refers to the actual buildings. (To me. Maybe someone else out there feels differently). You can't cancel a building, but you can close one.
However, when you say "school is canceled," (notice that it's singular), the word "school" refers to the concept of school (taking classes, studying, etc.), and not to the building itself. You can cancel all of the activities that happen inside of a school, so that's why "school is canceled" is ok.
When you say "school is canceled," you could be talking about just your school, or other schools in the area as well, since they will probably close too.
As for why "school" refers to the concept of school and "schools" refers to buildings/locations, that's a harder question that I'm not sure I can explain. But in English, when we say "go to school," of course you have to go to a physical building, but the phrase again refers more to the concept of school. To talk about the building in the singular, you'd say "school building."
Again, these are just my thoughts after a few minutes of thinking about the question. As is usual with language, others may have a different intuition.