Whisk flour, sugar, and salt together. Cut in cold vegan butter until pea-sized pieces remain.
Stir together 5 tablespoons ice water and apple cider vinegar. Add gradually to the flour mixture until a dough forms. Add the remaining water only if necessary.
Form dough into a disk, wrap, and refrigerate for 30 minutes.
Meanwhile, combine pumpkin puree, brown sugar, flour, cinnamon, ginger, nutmeg, cloves, vanilla, and salt in a saucepan. Cook over medium-low heat for 4 to 5 minutes, stirring frequently, until slightly thickened. Cool completely.
Preheat oven to 375°F (190°C) and line a baking sheet with parchment.
Divide chilled dough in half. Roll each portion between parchment to approximately 1/8 inch thick.
Cut dough into approximately 3 x 4-inch rectangles.
Place half the rectangles on the prepared baking sheet. Add about 1 1/2 tablespoons pumpkin filling to the center of each, leaving a border around the edges.
Place remaining pastry rectangles over the filling. Press edges together, then crimp with a fork.
Make several small vents in the top of each pop tart.
Bake for 20 to 24 minutes, until lightly golden around the edges.
Cool completely on a wire rack.
Whisk powdered sugar, plant milk, vanilla, and cinnamon together to make the glaze.
Spread glaze over cooled pop tarts and allow to set for 15 to 20 minutes before serving.