Most dogs will not pee or poop in their crate. They're different from cats that way. You are not doing her any favors by trying to get her to make a mess in her kennel. If you keep her in there for hours on end, of course she isn't going to potty in there. (Dogs are social animals. She should be playing with your family most of the day, and sleeping in her kennel if you're gone.) If you start her on any sort of pee pads or fake grass, you're going to create a problem for yourself because she won't go outside then -- ever.
I have a chihuahua. She is almost 20 years old. She doesn't have any problem holding it. The theory that they have a smaller bladder so they can't hold it is wrong. They have a smaller bladder but they also make less pee. My old doggie can hold it for hours and hours if she has to. She sleeps on my bed at night and holds it for at least 8 hours.
If she's cold, you need to get her a sweater and take her outside and stand there with her -- or better yet take her for a walk -- until she goes. Put some of the poop outside where you want her to go. My dog doesn't go very far from the back door these days. She has one spot she goes on outside.
You have to be consistent with this type of training. She has to be taught to go potty outside, even if it's cold and even if you're freezing standing there too. That's the crappy part about getting a puppy in the winter.