I'm trying to design a planet with two continents where one is always warm/hot and the other is cool/cold. The continents should be directly opposite each other (so not a pole and an equatorial one). They should by separated by some kind of barrier that is very hard but not impossible to cross (I'm imagining a large ocean but it could be anything that works, high mountains, expanse of volcanic fields, extreme weather, etc). Each continent can be either one large landmass or several smaller ones clustered together.
I don't want a tidally locked planet because a) I want day/night cycles and b) I don't want extreme heat and cold. Both continents should be habitable by human societies that have adapted to their climate without major technological intervention.
Basically one continent should have a constant Scandinavian winter climate with lots of snow but where you can still go outside wearing normal winter gear, and the other should have a constant hot climate, say Mediterranean or southern US summer. The hot continent can be tropical or dry or a mix, it doesn't matter as long as it's habitable (i.e. not just one massive desert). The continents can have seasons as long as they are mild - the hot continent's winter should still be warmer than the cold continent's summer.
Would it be enough to just make the cold continent at a much higher altitude than the hot one? Or is there a way to tilt the axis of the planet so that one hemisphere has very long hot summers and short mild winters while the other has long cold winters and short cool summers (not long enough to melt the snow)?
The climate difference is necessary for aesthetic/plot reasons but this is not a hard sci-fi world so a certain amount of fudging would be OK. I just want to figure out in my own head roughly how it could work.