According to a CBC article, the Irving Saint John refinery gets about 55% of it oil from the US, about 21% from Saudi Arabia and the rest from Nigeria. About 80% of its product goes to the US.
A refinery in Churchill would make no sense. A refinery cannot operate efficiently on a stop-and-start basis and with the port icebound for a significant part of the year, you would either need a lot - a real lot - of storage or risk losing your operating personnel for many months out of the year.
As much an additional export terminal is a good idea, it would have to be finished products (or gas) that can be moved or re-directed as the season allows. I can see either ice-hardened tankers and/or CCG escorts to extend the season, but that adds to the cost. It could also reduce cots for shipping diesel and LNG to the eastern Canadian arctic.
Moving some energy products, as well as improving the export market for prairie grain and potash can make for a viable port, but I don't see it as a savior project that moves the dial a great deal as some politicians and proponents due. Same with, in my mind, the fantasy proposals of putting a terminal in Moosonee, simply because it has a rail line.