Relevant section on Wikipedia:

The government may not criminally punish immigrants based on speech that would be protected if said by a citizen.[83] On entry across borders, the government may bar non-citizens from the United States based on their speech, even if that speech would have been protected if said by a citizen.[84] Speech rules as to deportation, on the other hand, are unclear.[85] Lower courts are divided on the question, while the leading cases on the subject are from the Red Scare.

https://en.wikipedia.org/wiki/United_States_free_speech_exceptions

Regarding the protections against illegal searches, I think all bets are off, even for US citizens.

To anyone wondering. Sauna boats are not common in Norway. It’s not “a thing”. Please don’t add it to the list of Scandinavian stereotypes 🙏