1. Winnipeg in December... wow... I haven't ever lived there myself, but the reputation amongst the rest of Canada is that anywhere in the prairie provinces during the winter is terrifyingly cold.
2. See if you can get the book "From the Ground Up" You'll be going through this book (or something very similar) during ground school and it has everything you need for the very basics. The other book you'll use is "Flight Training Manual" from Transport Canada, but I find it less useful.
3. Putting aside cold-weather operations for airplanes, for yourself, there's really not much. Jackets, boots, gloves, and things like that you can (should) buy here.
4. There really isn't any way to "save money" during flight training. Do read up on exercises and plans before you fly. Think about your flight after you've landed. There's ground-based simulators for part of your instrument time but I've never used one. Most importantly is to know what you're going to do before you do it, and make sure your instructor is clear on what you want to learn. I've had problems with instructors before, so I emphasize the need for clear communication.