Potty Training

Beanie (10 weeks old) is having a very hard time with her potty training. She frequently pees and poops on the carpet inside my home. I have been taking her out as often as I can, but she refuses to go outside! Sometimes, we are out for half an hour at a time and she still will not go. However, once we are back inside, she will bolt off to do her business in random corners of my house!

Also, seeing as how I live in the wonderful, but awfully cold, Canada, it's difficult to be with her outside for prolonged periods. I was wondering if I should try paper training her, and then trying again to tell her to go outside in the warmer months? It's very cold outside and I'm afraid that she's going to catch a cold being the wee pup that she is. It also doesn't help that it started snowing heavily about an hour ago!

I'm really getting very stressed out, and would appreciate any advice or comments!