If you become a GP you can get a job pretty much anywhere you want in Canada. We need doctors! If you specialize you will still have amazing job prospects. If you become any kind of doctor, don't even worry about finding a job. People will be fighting for you.
As for your view on hunting, if you are that opposed to it I'd say stick to a very large city. A lot of people hunt all across the country, so at least in large cities you won't cross paths with hunters.
So, you want mountains and oceans. That pretty much limits you to BC. However, BC ggets a LOT of rain. That said, the it isn't very cold there compared to the rest of the country. If you can stand the rain, it is great. Vancouver is expensive to live in, though. But there are, of course, lots of places to live outside Van.
The province of Quebec is also a great place to ski. There are some mountains there, but they're not like the Rocky's. I wouldn't move to Quebec unless you are fluent in French, unless you move to Montreal. But, Montrealers can be quite rude to anglophones. There is a huge french vs english mentality in Montreal. So beware!
You said you don't like cold weather, so do NOT move to any of the territories, northern parts of any provinces, or Alberta, Saskatchewan or Manitoba. If you move to the praries (AB, SK, MB) you will surely freeze. It gets sooo cold in the praries in the winter, even in the southern parts of those provinces. Just to give you an idea of how cold it gets in the praries. If you were to move to Winnipeg, a city in southern Manitoba (and so warmer than other parts of the praries simply because it is a city), in one day in February one year it was --48 degrees celcius. That is --54 degrees ferenheit, I believe. That is before accounting for the windchill, so it would have felt like a hell of a lot colder. One day in 1996 it went down --57.1 degrees celcius with the windchill. So long story short, stay out of the prairies.
Southern Ontario is warm, relatively dry, cheap to live in (except Toronto), not hectic (except Toronto), and beautiful (except Toronto). However, Southern Ontario doesn't have mountains or an ocean view. We do, however, have the great lakes. Central Ontario has a TON of hunters, tho. There are some towns where the men don't seem to take off their hunting gear even when it isn't hunting season. (btw, you won't find a ten year old shooting a deer. you have to be 16 to get a gun licence.. you might find a kid with a cross bow though haha.)
So where should you move?
If you can bear the rain, go to BC...but stay out of Vancouver.
Or, if you speak French or are willing to pick it up and can sacrifice an ocean view, go to Quebec (Quebec city).
Or, if you can sacrifice the mountains and live with a million lakes rather than the ocean, move to southern Ontario. Guelph, Waterloo, Barrie, Stratford, St. Catherines, and Peterborough are all great places to live in southern ontario.
Or, if you can