Mix the wine, lemon juice, honey, mustard, salt, and pepper in a blender. With the machine running gradually blend in the oil. Season the vinaigrette to taste with more salt and pepper, if desired.
In a large bowl combine the arugula, endive, and walnuts. Toss with 1/4 cup of the vinaigrette to coat and adding more vinaigrette, if desired. Serve immediately. Any remaining vinaigrette can be saved in an airtight container in the refrigerator for 3 days and should be brought up to room temperature before using.