In case you haven't booked your ticket yet, local (=in ushuaia) purchase of an 11 day antarctic trip (they call it "last minute") costs between 3500 and 4000 usd depending o the boat/company, that is half of the price advertised on the tour operators websites. I had booked one, it was cancelled for technical reasons, and as it was the end of the season I could not get another seat... saved me $$$, but I would have liked to go.
Now to answer your question: the tourist agency where I had booked my ticket, in Ushuaia, was providing the boots and coat (which indeed are not provided onboard). Google a few tourist agencies and ask them if they can rent you the equipment. Otherwise I'll try to find the name of the one I went to.

I must be damned with boats, another 3 day boat journey I had booked up the chilean coast has been cancelled for technical reasons...