I don't really like vodka Martinis, they just aren't right. Now that's off my chest let's look at the advantage of the vodka Martini. Its an easy base to work from and you can infuse vodka with all manner of tastes, including Mince pie. Yup mince pie.
Get some good mincemeat (like this) and put 4 good table spoons into a bottle of vodka, leave 48 hours and your vodka should turn a pale gold colour, strain out the fruit (you may need to filter spices & stuff too) and enjoy.
Or make a Christmas Martini
There were a couple of inspirations here, including a random conversation about bitters heavy drinks, you can make this without all the bitters, but they really help intensify the mince pie flavour.
2 dashes Angastoura Bitters
2 dashes Peychauds Bitters
2 dashes Orange Bitters
2 dashes Chocolate bitters
3 Parts mince pie Vodka
1 Part Noily Prat vermouth
Stir down over ice, strain & garnish with a cherry
Enjoy the extra winter cheer