Hi Lucinda,
On this trip you'll be travelling to Churchill where the average high in October is 1 degree and as you are travelling at the end of the month it's probably worth considering that the average high for November is -9!
I would recommend that you pack warm layers (layers will help to trap bodyheat while you are out, and when back at the lodge you can remove a layer if you get too warm), hat, gloves, scarf and a waterproof anorak. In terms of footwear, sturdy walking shoes/boots suitable for cold climates.
Kindest regards,
Julia