I’m saying this with my tongue in cheek - but ...
The furthest edge of the current Antarctic sea ice extent is 58-59 degrees south latitude at its maximum in mid-September. Cape Horn is at 56 south latitude, so the “average” edge of the Antarctic ice pack “only” has to go another 2 degrees latitude to close the strait to commercial traffic - not ice breakers of course.
Unlikely? Of course. The peninsula curves towards South America, but the ice at that closest spot tends to flow to the east and so the actual maximum area is a bit east of the straits. probably will stay that way. But it is fun to bug the CAGW crowd with that question.
(At Antarctic minimum, the Antarctic sea ice is just at the Antarctic circle at 66-67 south latitude. Arctic sea ice is all between 72 north and the pole. Except for Hudson Bay and the Bering Sea - both very small compared to the Arctic. )