In the bowl of a stand mixer, cream together the softened cream cheese, mustard, and horseradish until evenly incorporated and the mixture's smooth.
Spread a quarter of the mixture evenly out over the under side of one of the flour tortillas. Repeat with the remaining tortillas, until the cream cheese is gone.
Layer slices of roast beef evenly out over top the cream cheese mixture. Cover almost the entire tortilla leaving just a little bit of the edges clean.
Divide the cheese ball into four quarters and spread a quarter out evenly over the roast beef on top of each tortilla.
Spread a single layer of spinach leaves out over top to cover the roast beef.
Starting at one end tightly (but without squishinroll up the tortilla. Sit the tortilla with the end piece on the bottom.
Using a sharp serrated knife, cut the stuffed tortillas into 1" slices. Use tooth picks to secure if needed.
Serve immediately or refrigerate the pinwheels, covered, until ready to serve.
Notes
For perfect, pretty slicing-- chill the filled and rolled tortillas for 5-10 minutes before hand.