From what I've seen online, Finnish winters don't seem to be any worse than Minneapolis, which will have tent encampments all through winter. They often aren't broken up and forced into shelters unless we get an especially bad cold snap; activists argue that forcing people out of tents means they lose possessions and are worse off.
https://www.cbsnews.com/minnesota/news/we-just-want-to-be-wa...
https://www.kare11.com/article/news/local/homeless-camp-resi...
There's a very tough residence among the "permanent" homeless to any program that offers housing, because it will come with some strings attached. Those with mental health issues fear (wrongly) that they will be involuntarily committed to an asylum or something similar. Others don't want to be forced to try to get a job, or give up drugs.
The "temporary" homeless can, and do, make use of the help the government and non-profit organizations provide. Job training, free bus passes, assistance with rent, food, hygiene etc.
Some in-between will always float back and forth. If they stick to their medicine, they can live pretty independently, but since they don't like the side effects, sooner or later they stop, have a psychotic break, and end up back on the street until a family member finds them and convinced them to get help again.
At least, this is my understanding from someone who works for a program whose funding and sole mission is to the homeless in Minneapolis.