My guess would be that a reindeer doesn't give much volume of milk. When you compare the different breeds of cows, the ones that are the high producers also have the lowest butterfat content. So Holsteins, while they can give up to 8-10 gallons a day, are the lowest commercial butterfat content cows. Beef cows, on the other hand, have a typically high butterfat content, but produce more in the range of 1-2 gallons per day. They aren't as persistent in their lactations, either, usually drying themselves up in 9-10 months, while a Jersey can go for a couple of years, if desired.
Just a few more cow facts for you!