Dairy cattle are always pregnant. No baby, no milk.
The regulations in Austalia and NZ for dairy cattle are very strict. Adding synthetic hormones to dairy cattle has been banned in Aus for a number of years. Cattle are only allowed to even be treated by antibiotics if they are sick and then the milk from that cow cannot be sold for a certain period of time.
Natural oestrogen levels are at there highest in the last couple of months before birth and most farmers generally stop milking them about 60 days prior. The amount of cow oestrogen that gets in to a normal glass of full cream milk is in the nanograms and is almost negligable in low fat milk and there is no proof it has any effect on humans.
