Depends on what a "foreigner" is classified as

We can't ban house ownership to refugees, permanent residents, immigrants who are waiting for citizenship, ambassadors, consulates and such, because that would have catastrophic consequences for the country, as well as international relations with other countries. If you mean people who speculate, and don't actually live here, but sit on a property just because it's valuable, then yes, because nobody's living in those houses anyway.
However, there should be consultation with places that have a large amount of vacation homes, nd rely on that for tax money, because they need it for their municipal budgets and it could harm their ability to invest in their community very much.