Is pumpkin pie a Christmas dessert?

You guys already know that I only eat seasonally themed desserts. Occasionally, people will be surprised when I tell them I don't consider pumpkin pie a Christmas dessert, only a Halloween and Thanksgiving dessert. So what do you think? There is a poll on the sidebar. (It doesn't show up in mobile view; if you want to see it on your phone, you have to click web view.)

I have put a lot of thought--maybe too much thought--into this. So here are arguments for and against pumpkin pie for Christmas.

Pumpkin pie as only a fall dessert

• Pumpkin is a symbol of harvest, Halloween, and Thanksgiving. Not a symbol of Christmas.
• If I consider something to be a dessert for a holiday, I consider its variations also suitable for the holiday. Since red velvet cake is a Valentine's Day dessert, any red velvet item is suitable for the holiday. The vast majority of pumpkin pie themed items (such as Pop-Tarts) are marketed for the autumn, not for Christmas, and they often go on clearance as soon as Halloween is over (which is still too early). (There are a few pumpkin items marketed for Christmas; Spiced Pumpkin Pie Clif Bars are decorated with snowflakes on the wrapper.)
• The Oxford English Dictionary's entry for pumpkin pie mentions only Thanksgiving, not Christmas. (It also doesn't mention Halloween, even though I consider it suitable for Halloween.)
• Christmas already has tons of sweets, what with gingerbread, peppermint, eggnog, sugar cookies, hot chocolate, etc. It doesn't need more.

Pumpkin pie as also a Christmas dessert

• Just because pumpkin pie is undeniably a Thanksgiving dessert doesn't mean it's only for Thanksgiving. I mean, I already count it for Halloween. I consider candy corn suitable for both Halloween and Thanksgiving, even though it's more Halloweeny. 
• The spices of pumpkin pie are also the spices of Christmas. (However, you can get them other ways at Christmas, such as gingerbread, wassail, and eggnog, and spices do not equal Christmas. Carrot cake isn't a Christmas dessert.)
• Pumpkin pie has been present at many Christmas parties (but so have decidedly non-Christmas desserts).
• Pumpkin pie is mentioned in a few Christmas songs: "Pennsylvania and some homemade pumpkin pie," "later we'll have some pumpkin pie, and we'll do some caroling," "when they pass around the coffee and the pumpkin pie." (However, "Rockin' around the Christmas Tree" is the only explicitly Christmas song; "Home for the Holidays" doesn't specify what holidays, and "Sleigh Ride" is only a winter song. Coffee certainly isn't a Christmas thing, even though it's in the same line.)
• Many people tell me I should count pumpkin pie as a Christmas dessert. (However, they almost always refer to the above songs, so this shouldn't really be its own argument.)
• There is considerable overlap between Thanksgiving and Christmas on the culinary side, with cranberries, cider, turkey, etc. (I've found, though, that when people say "Thanksgiving and Christmas go together," they use it as an excuse to have Christmas trees at Thanksgiving, and never Pilgrims at Christmas.)
• Counting it as a Christmas dessert would enable me to have it after Thanksgiving. (Currently I won't even eat it the day after Thanksgiving.)

What do you think?