Bring the vinegar to a simmer in a saucepan over medium heat. Add the celery and carrots. Remove the pan from the heat. Set aside to cool.
When the vinegar is cool, add the bell peppers. Cover and refrigerate until cold.
Strain the chilled vegetables through a sieve. Reserve the vegetables and save the vinegar for another use.
Mix together the apple, cucumber, treviso, arugula, and cabbage in a large bowl. Add dressing and toss well. Season to taste with salt and pepper. Add the goat cheese and almonds to the bowl and toss to mix. Divide among 6 small bowls or plates.