On top of that, most of that water is excreted again - otherwise, your cow would gain 640lbs a day. Or, with the 1000 gallons/gallon of milk scenario, some 12,000 lbs/day
Assuming that that water is tap water is also... well, a most pessimistic assumption.
If you wish a quick sanity check of your numbers, US milk production is ~25 bln gallons/year. Roughly ~70 mln gallon/day. Assuming it took one day at 10kW for a gallon of milk, that'd be 700GW continuous energy consumption for our annual milk production. This is a substantial part of the total US energy production.
Second check: Assuming really cheap energy ($0.09/kWh, 10kW, 24h), that gives us a milk energy price of ~$21.00/gallon. Just the energy. This does not quite match, either. $14/gallon if you go exclusively with wind energy, which is IIRC the cheapest right now.