One of the most important factors restricting tomatoes to thrive in Northern climates is the setting of the flowers. In most varieties the setting of flowers requires a specific temperature range. Too cold or warm and the flowers do not set resulting in no fruit. Cold-tolerant varieties often set flowers at lower temperatures. Another typical feature of the growing season in the north and far south is that the growing season is short. This restricts the varieties you can grow to early varieties. There are ways to grow also other varieties, which usually requires to start your tomato seedlings inside or in a heated greenhouse well in advance to the last frost date when the seedlings can be moved outside.
Tomatoes cannot tolerate any frost. Even temperatures below 10C often results in plants sulking and going into a growth arrest. Exposure for longer periods to low temperatures often result in the inability of the plant to recover. The leaves can turn almost blue and the plants just sit there. The ability to tolerate lower temperatures is entirely dependent on the variety. Some varieties tolerate some cold weather, others wither away after even a short exposure to the cold. Wrapping up the plants in cloth or other materials may help plants to endure unexpected cold days.
On the other end of the spectrum too warm is also not good. Extreme hot weather in combination with moisture can end the life of any tomato plant.
Because the tomato originates from a warm climate they usually do not deal with cold temperatures at all. Although varieties have been developed to deal with colder climates.