All highlighting is mine
Concerning calving in the middle ages,
Cows...would calve in the
early spring. Calves would nurse for about a month and then be
separated from their mothers and fed by hand until they learned to
graze on their own. Ideally, the calves would be weaned just as the
pastures began showing some good growth, but in a cold spring the
farmer would just have to hope he had enough hay stored up.
E. Griffiths & M. Overton in Farming to Halves also state that calving was in spring. Peter R. Coss, in Thirteenth Century England IV, says that
the medieval cow was not generally added to breeding stock until she
had reached her fourth year, probably because the animals were
undernourished and slow-growing.
On the consumption of milk, Melitta Weiss Adamson in Food in Medieval Times says
In the Middle Ages, infants were fed the breast milk of mothers and
wet nurses, and animal milk after they were weaned. Cow's milk was the
most common milk.
The Wikipedia article on Medieval Cuisine adds,
Plain fresh milk was not consumed by adults except the poor or sick,
and was usually reserved for the very young or elderly.
Peasants were more likely to drink milk than wealthy adults and it had other uses too:
milk was used for a lot of cooking, even on days when fasting
prohibited to consumption of animal meats and fats. Milk was seen to
have medicinal properties too, and many physicians recommended it for
ailments. However, it was advised to not drink milk and alcohol
together, as the combination may cause a belly ache and diarrhea.
Milk, of course, is perishable so
Before refrigeration and pasteurization, the most common methods of
extending the shelf-life of this highly perishable foodstuff was to
turn it into butter or cheese.
You may also be interested in this article Lactose Intolerance in the Middle Ages (it was at a similar level to today).