Cook pine nuts in a 6- to 8-inch frying pan over medium heat, shaking pan often to stir nuts until pale gold, 2 to 3 minutes. Pour from pan.
With a knife, cut peel and membrane from grapefruit. Holding fruit over a bowl, cut between segments and inner membrane to release fruit into bowl. Squeeze juice from membrane into bowl; discard membrane.
Rinse Fuyu persimmons, trim off and discard stem ends, then slice fruit crosswise into thin rounds.
Rinse Asian pears and discard stems. Cut fruit crosswise into thin rounds through center seeds. Coat pear slices with grapefruit juice.
In a small bowl, mix 6 tablespoons grapefruit juice (reserve remainder for other uses) with lime juice, rice vinegar, and honey.
Line a salad bowl or salad plates with frisee. Arrange Fuyu persimmons, Asian pears, and grapefruit on frisée. Sprinkle with pomegranate seeds and pine nuts, then moisten with the grapefruit-lime dressing. Add salt to taste.