Wrong. Freezing temperatures are by far the most challenging environments for plants to deal with and only a limited set of species are well adapted for cold climates. Meanwhile warm climates mean year round growing seasons and the widest range of species that thrive, this is why you can grow almost anything in tropical zones and get much more productivity out of that growth.
Hardiness zones are really useful for human cultivated plants. Many seeds require a certain amount of time below a low temperature to germinate and a hundred other variables. You seem to also be assuming many biomes in the northern hemisphere turns into a rainforest rather than a desert from increasing temperatures.
See: https://www.gilmour.com/planting-zones-hardiness-map