I'm not entirely sure that the US would make much money selling dairy to Canada even without the tariffs to be honest.
It was mentioned earlier, but in Canada you're not allowed to sell dairy products pumped full of growth hormones as is typical of US dairy. There are different standards in different provinces, but antibiotic usage in Canada is much more strictly measured and tested than in the US. Because of this, most of the milk currently made in the US wouldn't be eligible for sale across the border anyway . . . so I don't believe that there would be significant benefit to Canadian consumers.
Which is all the more reason to remove the tariffs! Very few mass producers in the USA are interested in producing to those standards, but some do already. Why not let them in? The Canadian consumer would benefit through lower prices and greater selection.
The way that the tariffs on dairy in Canada is implemented, it is just a government enforced wealth transfer from the consumer to the producer.
My dad's a farmer, and I've had a long time to think about Canada's rather odd milk quota system. It has quite a history, starting back in the 50s I believe as a supply management idea. There are arguments for and against it, but generally the one given for it is thus:
If the US was given full, unfettered access to Canadian dairy markets, there would no longer be any Canadian dairy farmers. I bet that within a year they would entirely be wiped out. This becomes a pretty serious problem if several years down the road there's a shortage in milk products in the US. You can't just create a new dairy farm in a couple months to meet that demand. That's why we have supply management on several food items (dairy, eggs, chicken).
It's also important to note that the US has always had tariffs on dairy going into the country from Canada (in the range of 17 - 20% if I remember correctly). It's weird that Trump is demanding an end to Canadian tariffs but staying quiet about the US ones.
My Dad was a dairy farmer, we lost the farm when I was 12. At the time there was consolidation in the industry, you had to buy quota to expand or you left. Few people remember the losers of the quota system, 90% of dairy farms have closed over the last 30 years. Not everyone in the industry enjoys the quota system, just the 10% that remain. The farmer who bought our quota closed 6 years later.
The argument for Quota is interesting when you compare it to pork and beef which are integrated with the USA. Eggs and chicken are quota, but pork isn't; no one is able to explain that logic. Tell me why porkchops are exempt but nuggets are sacred; my answer is the chicken council is hiding behind the dairy council because they know they don't have a drumstick to stand on. Pig production takes longer to ramp up then chicken, as witnessed in the swine fu and avian flu epidemics, both of which are recent events.
I gurantee dairy would remain in Canada, but not every dairy would survive. The cost to ship 2% milk from wisconsin to my house prevents whole milk making it to my local grocery store, theres a natural protection. Cheese on the other hand is dense, that's the market Americans are after.
When dealing with low value products that are heavy such as milk, logistics is a big cost. Sourcing them near the end user makes sense, just to save on shipping costs. Evrey province in Canada has Chicken, Dairy and eggs, because of shipping costs between provinces. Wisonsin and California have massive Dairies, but I bet every state has some dairy production for the same reason that every province does.