Question- what type of winter do you experience where you live? Here it's winter boot season- so the first thing the kids do when they get to the classroom is change shoes.
Come to think of it- until 7th grade, we always had to bring a pair of 'inside shoes' to school- no black soles. Where I grew up we had some pretty extreme weather- snow, rain, etc- and I guess they didn't want us tracking snow and mud everywhere (especially since a lot of the classrooms were carpeted). The only time you could really get away with not wearing your 'inside shoes' was at the beginning of the year and the very end of the year- when the ground was fairly dry. Any other time- you would go around in stocking feet 
Either way- I wouldnt worry about the threat of your daughter catching anything. You dont know how long the vomit had been there (could have been the result of a drunkard the previous night), or if the person was 'contagious' sick or sick due to motionsickness, etc.
Still gross though! EWW
*amber*
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