1,400 gallons per day (including rainwater)
According to "The green, blue and grey water footprint of crops and derived crop products" (Mekonnen and Hoekstra, 2011), for the period from 1996 to 2005 the global average water usage for fodder crops was 253 cubic meters per ton (or 253 L per kg).
Your original source gives a range of 18 to 25 kg/day for fodder consumed by a lactating cow. Using that range, the water needed to produce that amount of fodder per cow is between 4,554 and 6,325 liters of water per day. That's an average of about 1,400 gallons per day.
Here's the breakdown by water type:
- 27 liters/kg blue water: "the volume of surface and groundwater consumed (evaporated) as a result of the production of a good" (this includes irrigation water)
- 207 liters/kg green water: "the rain-water consumed"
- 20 liters/kg grey water: "the volume of freshwater that is required to assimilate the load of pollutants based on existing ambient water quality standards."
460 gallons per day with rainwater ignored
If we want to take rainwater out of the equation, the full 1200 page report from the Water Footprint Network includes an annual breakdown for the U.S. of water usage by type for fodder production:
Green (rainfed): 154,374.1 Mm3/yr
Green (irrigated): 15,933.7
Green (total): 170,308.1
Blue (irrigated): 30,923.2
Thus, rainwater makes up about 68% of the total. Reducing the total above by this fraction gives a range of 1,457 to 2,024 liters per day, or around 460 gallons per day.
What the cows are drinking
According to the U.S. Geological Survey, the median dairy cow drinks about 35 gallons (132 liters) per day. A mere pittance compared to the water in their feed!