One reason I feel intimidated is the winter weather, as I don’t know
how to cope with it.
Warm clothes. You don't mention any location (or any other information) in your profile so I have no idea what kind of climate you are used to. But you only mention places in the south, so the weather will likely not be very harsh.
It’s my first time visiting Sweden, and I’m also unsure where to find
affordable housing.
Hostels can be a good option for longer stays.
I plan to visit Stockholm, Malmö, and Gothenburg.
Why have you choosen them and what are your goals for this trip?
I love doing arts and crafts, playing badminton, and hiking (though
I’m not sure if hiking is a good idea in winter).
Hiking isn't really a big thing in the winter, many hiking trails become ski tracks in the winter.