First I want to say that 7 billions people doesn't celebrate christmas, it's only about 2 billions. Also I want to say that the cookies and milk aren't per person, they are per family (each normal family has 4 persons). And finally I want to say that in a lot of contries people don't put food or they but others things like chocolate or marzipan.
Respect
Santa doesn't eat cookies or drink milk, maybe he do that but he don't consume all the cookies and milk he gets, he only eat like a human, then he throw away the rest of the food so people get happy that Santa "eat" the cookies...
Squirell (Food for winter)
Santa doesn't eat the food in one day, he do like the squirells, they store food for the winter. Santa store all the cookies and milk in the bag when he drop the presents for the 364 remainings days of the year. I don't think that milk would rotten, he is the North Pole.
Gift / Food for they minions
Santa has a lot of minions (AKA: elves). He store in his bag the cookies (and in a tank the milk?) and when he reach to the North Pole he gift to his minions all the food for their hard work.
Even he can feed their minions with only cookies and milk, see my calculations:
$$ \frac{2,000,000,000 \text{ Believers}}{4 \text{ Believers/family}} = 500,000,000 \text{ Families}$$
$$ 500,000,000 \text{ Families} \times 3 \text{ Cookies} = 1,500,000,000 \text{ Cookies}$$
$$ 500,000,000 \text{ Families} \times 1 \text{ Glass of milk} = 500,000,000 \text{ Glasses of milk}$$
$$ \frac{500,000,000 \text{ Glasses of milk} \times 200 \text{ ml/glass}}{1,000 \text{ ml/litre}} = 100,000,000 \text{ Litres of milk}$$
$$100,000,000 \text{ Litres of milk} \times 1.032 \text{ kg/l} \times 420 \text{ Calories/litre} = 43,344,000,000 \text{ Cal}$$
$$ \frac{1,500,000,000 \text{ Cookies} \times 8 \text{ gr/cookie}}{100 \text{ gr}} \times 353 \text{ Calories/cookie} = 42,360,000,000 \text{ Cal}$$
$$ 42,360,000,000 \text{ Cal} + 43,344,000,000 \text{ Cal} = 85,704,000,000 \text{ Cal}$$
$$ \frac{85,704,000,000 \text{ Cal}}{365 \text{ days/year}} = 234,805,479.45 \text{ Cal/day}$$
$$ \frac{234,805,479.45 \text{ Cal/day}}{2,000 \text{ Cal/day}} = 117,402.73 \text{ Humans}$$
I don't know the dayly calories that need elves but Santa is capable of feed more that 100.000 humans only with cookies and milk! (And yes, I checked the water values of milk (87%), they won't die of thirst).
Also we can calculate the fat value:
$$ \frac{\frac{1,500,000,000 \text{ Cookies} \times 8 \text{ gr/cookie}}{100 \text{ gr}} \times 16 \text{ gr/fat}}{1,000 \text{ gr/kg}} = 1,920,000 \text{ kg of fat}$$
$$ \frac{\frac{100,000,000 \text{ Litres of milk} \times 1,032 \text{gr/l}}{100 \text{ gr}} \times 1 \text{ gr/fat}}{1,000 \text{ gr/kg}} = 1,032,000 \text{ kg of fat}$$
$$ \frac{\frac{1,920,000 \text{ kg of fat} + 1,032,000 \text{kg of fat}}{365 \text{ days/year}}}{117.402,73 \text{ Humans}} \times 1,000 \text{ gr/kg} = 68.88 \text{ gr/day of fat}$$
68.88 gr of fat per day don't kill anyone! They are healthy values! Well, for been exactly for a person who doesn't do physical activities it's bad, but not lethal.
And if you want about their cholesterol amount:
$$ \frac{\frac{1,500,000,000 \text{ Cookies} \times 8 \text{ gr/cookie}}{100 \text{ gr}} \times 3 \text{ mg/cholesterol}}{1,000,000 \text{ mg/kg}} = 360 \text{ kg of cholesterol}$$
$$ \frac{\frac{100,000,000 \text{ Litres of milk} \times 1,032 \text{ gr/l}}{100 \text{ gr}} \times 5 \text{ mg/cholesterol}}{1,000,000 \text{ mg/kg}} = 5,160 \text{ kg of fat}$$
$$ \frac{\frac{360 \text{ kg of choresterol} + 5,160 \text{ kg of choresterol}}{365 \text{ days/year}}}{117.402,73 \text{ Humans}} \times 1,000,000 \text{ mg/kg}= 128.93 \text{ mg/day of cholesterol}$$
128.93 mg of cholesterol per day don't kill anyone! They are healthy values!
Biofuel
Santa use all the organic matter from food to make biofuel! He lives in the middle of nowhere (North Pole), How he get power? He can use biofuel in generators to produce electricity.
Like I said before he gets $85,704,000,000 \text{ Cal}$ in food.
$$ \frac{\frac{\frac{85,704,000,000 \text{ Cal} \times 4,184 \text{ Joules}}{365 \text{ days/year}}}{24 \text{hours/day}}}{1,000,000,000 \text{ W/GW}} = 40.93 \text{ GW/h}$$
Enought to power several cities... for an entire year. Well, obviously motors and generators aren't 100% efficients so you can split the number in 2, also I am not sure if cookies can be rotten and turn in fuel...