what kinds of foods should serve in cold weather birthday?

Depends on her age and how many individuals to serve, but here are some ideas:

Spaghetti & garlic bread or brushetta

Warm sandwiches:

Get some Hawaiin rolls, roast beef, cheese and toast them for hot sandwiches.

Toasted English muffins, turkey and have items like avocado, tomato, condiments.

Taco or fajita bar.

Chili & cornbread.

Clam chowder in mini sourdough bowls.

Mini corn dogs, sliders with option of hamburger & chicken.

Some type of soup/stew that is a favorite in your area but serve in a fun manner. I always loved (and still do) a fish stew.

Chicken noodle soup & grilled cheese.

Mini BBQ sandwiches, or BBQ and corn on the cob, etc.

Make mashed potatoes, top with pulled chicken and some creamed gravy.

Chicken dumplings.

Warmed cinnamon apples.

Mac N Cheese, add something like tuna or chicken or even do some Hamburger Helper and do your touch on it.

Homemade pizzas on English muffins, let them choose how to make it.

Mini Pizzas

Mini Quiches

Mini Sausage Rolls

Burgers

Hot Dogs

Chicken Legs/Wings

Chips/Fries

Small Cup of Soup with Crusty Bread

Hot Chocolate with Marshmallows and Cream

Warm Chocolate Brownies with Ice Cream

Hot Chocolate Fudge Cake with Ice Cream

Just regular finger foods. Sandwiches and chips. If they are going to g outside and play make up some hot chocolate and apple cider for when they come inside.