Just regarding the gym membership - do you live anywhere near a Planet Fitness? You can get a membership for a mere $10 a month, which is doable for almost anyone.
Regarding running outside in the winter... I now live in Northern New England, but used to live in Montreal. One winter, I trained for the 21k de Montreal, a half-marathon which is run in April. So, I did all of my training during the snowiest part of the winter. (And I agree mtlgirl, they do have an amazing snow removal system... the best I have ever seen.) Still, sidewalks remain icy. I did much of my training indoors, since I had access to a good gym, but I had to take it outside while snow was still on the ground, to get used to the roads in time for the race. For me, the biggest problem has never been the cold itself. In fact, I don't find that to be problematic at all. Wear a hat, wear non-cotton wicking clothes, dress in layers, wear underarmor, as others have said. By the way, Target has a fantastic line of inexpensive workout clothes - C9 by Champion. They sell compression shirts which work like magic... this year is the first year I have tried these. They're absolutely amazing in keeping you warm. But anyway, the biggest problem for me has always been my fear of falling... I'm not sure-footed running along on ice or in areas where there could be ice. So the top piece of advice is to get grippy running shoes! You can even buy YakTrax which are meant to be used over running shoes. A good investment. (Edit to add, just noticed the poster above me mentioned these too.)
Goal Weight: 130
Fitday member since 2004, forum member since 2010.