This is a nuanced issue and I agree with what you wrote. I live in Finland. Some additional thoughts:
- The scale of social problems in the US is on a whole other level. More people requires bigger solutions.
- The state vs government system in the US means it's every state for themselves when solving social issues. This is seen in states actively shipping homeless people to warmer climate states in order to make their problems go away.
- As you point out, homeless people die in the winter. It's also cold in many places in the US, and hot in others - so people die all the time there too.
- As a society Finland has a robust social security system, the society is built on it - and the idea of equality (Hint: its not, but it's not bad at all either compared to other countries). The amount of Americans I've seen arguing against free healthcare as they don't want to pay for it just blows my mind, I would imagine you'd go into a similar situation if the government raised taxes to "fix the homeless problem". "Well i'm not homeless, why should i pay for these people's problems" etc. (Not my view, just predicting how it will go).