Nobody will freeze to death waiting as temporary shelters are always available for everyone, exactly for that reason.

We do still have around 3500 homeless, around a thousand of who are categorized as "long term" and not just someone that's couch-surfing at their parents or friends while waiting for an a new apartment, but as everyone in Finland is eligible for enough social assistance that they could always pay rent and buy food, the majority of those 1000 are people who either refuse out of principle or have such bad drug addictions or mental health issues that they spend all that money on those or trash the places they are given and get kicked out.
And for those there isn't much anyone can do, as unless you commit enough crimes to get jail time you can't be forced to go to rehab, get treatment, or stop living on the streets either.

Here's an info page about it in English from the "No Fixed Abode NGO".