K.
I think the criteria for keeping home from school probably are different depending on whether you work or not, since for me, keeping my son at home means a lost day of work. (ie I'm more likely to send him slightly ill than a SAHM, perhaps. Not the way it should be, but this is reality).
For me, vomiting, diarrhea, fever, feeling visibly crappy+ some mild symptoms, fever + cough or any flu-like symptoms are a stay home. Runny nose and sneezing alone is not an automatic stay home - depends on how much sneezing, how much snot etc. Also would depend on his overall feeling (is he lethargic, or acting normal). Kids will chronically have a runny nose over the winter. It's just "daycare snot". Get used to it. I always call to let his preschool know that he will not be in that day.