Whirl cream cheese and feta in a food processor until smooth. Using a 1-in. ice cream scoop or a teaspoon, scoop balls of cheese mixture onto a plate. Chill 15 minutes. Pour almonds into a shallow bowl. Roll cheese balls in almonds to coat and set on a clean plate. Chill until firm, about 1 hour.
Whisk vinegar, oil, salt, and pepper in a large bowl to combine. Add greens and cherries and toss to coat. Arrange salad on plates and scatter cheese balls on top.
Make ahead: Through step 1, up to a few hours.