Answering this question from a pure economic point of view.
Assumptions and Inferences:
Total population of canada: ~40 million
Milk is consumed by people of all ages. Considering 2-3% of the population does not consume dairy products due to different reasons (lactose intolerance, vegan lifestyle, allergy, dislike, etc). This means ~39 million people in Canada consume milk in one form or another
Cow here refers only to the female which is used mainly for milk production. Meat/beef is obtained from the bull, which is not included in this estimation.
Per capita consumption of milk is about 0.3L per day. Averaging for throughout the year, per capita consumption of dairy products: butter/cheese, etc is about 20grams per day. It takes about 5 litres of milk to produce 1kg of cheese/butter. Therefore, it adds to 0.1L milk per day. In total, per capita consumption of milk (milk + dairy products), is about 0.4L per day. In total, the daily demand for milk is ~15.5 million litres (39 million * 0.4L).
On average, a cow produces 15-20 litres of milk per day. Therefore, the total number of cows in Canada amounts to 0.7-1 million. (15.5 million/20 or 15.5 million/15)