An article on Oilprice.com estimates the amount of switchgrass Santa's reindeer would consume using analogs to biofuel production, which has some interesting data but I dislike their analysis.
Useful data from his oil article includes:
- Santa needs to travel around 226 million miles to deliver all of the presents to the world’s children.
- We do know that mules and oxen can go roughly 15-20 miles per day.
- We also know that a typical livestock animal might need to eat around 1.5 percent - 2 percent of its bodyweight in forage feed (depending on the nutritional content of that feed).
- We also know that a male reindeer weights 350-400 pounds.
- Santa’s reindeer are probably on the more muscular end of that scale, meaning that they’d need to eat about 2 percent of 400 pounds, or 8 pounds to be able to fly 15-20 miles.
- Update. My assumptions were wrong, so I've updated this answer below!
So, this is "forage feed," your hay and grasses. According to Dayville Hay and Grain, 8 pounds of Hay (a mix of Alfalfa Hay and Timothy Hay, because we're running up against a lot of assumptions and estimates here) runs up to 7,124 calories.
So, the "fuel economy" of a single reindeer, dashing up and down hills (average them out to flat) is about 407 calories/mile (7124 / 17.5). Santa has 9 reindeer, so his sled's "fuel economy" is 3,664 calories/mile.
828,012,342,857 calories in mixed Alfalfa and Timothy Hay. This doesn't include trips back and forth to the North Pole, because I don't know what the sled capacity is for toys, and therefore I cannot calculate how many north pole trips would be required. With the fuel economy figures provided, you can add on however many additional miles you deem necessary.
Using the same reference material above, Santa's reindeer would need to eat **662,409,874 lb (331,204.937 short tons) of premium feed oats. That comes up to 73,601,097 lb (36,801 short tons) each!
Bonus round: To grow that much oatage you would need 103,501.5 acres of land, assuming a decent harvest for silage source. To get that much, you'd need to plant an area at least half the size of Rhode Island in nothing but Oats, just for consumption this one night.
ALSO UPDATE. According to the San Diego Zoo, reindeer would actually eat about double the numbers above. The exact numbers depend on the specific animal and their workload, but we can give an estimate of 1,324,819,748 lb (662,409 short tons) of premium feed oats. This would require oat production across the entire state of Rhode Island to produce the food burned this one night.