Peppermint is a standard syrup at Starbucks - not seasonal. (Even if the peppermint mocha is not on the menu, you can ask for it. It's like In-And-Out Burger...there's a "secret" menu. Like a "grasshopper" - a peppermint green tea latte which you can get whenever. I just had one after yoga today.)
Gingerbread and Pumpkin are season-specific.
I have worked at Starbucks and one of my best friends is a manager, and the lack of peppermint year-round is one of the most common misconceptions going.