DRESSING: Put the vinegar, mustard, and celery seeds into a medium bowl and whisk to combine. Season with salt to taste. Add the sugar and whisk vigorously until dissolved. Pour the vegetable oil in a thin stream into the bowl while whisking constantly, until it is well combined with the other ingredients and a smooth dressing is formed. Season with salt to taste and set aside.
COLESLAW: Put the green and red cabbages and carrots into a large bowl. Add the dressing and toss well to combine. Store the coleslaw in the refrigerator until ready to use, up to 1 day. Serve chilled.