Is the only time you ask her to leave her crate when you want her to go outside? What's her body language when you approach her while she's crated? Does she freeze up? Pant? Get bug eyed and/or slick her ears back? Lick her lips? Turn her head away from you?

Does she have a coat to wear? Boots? Salt from sidewalks burns paws.

Has something happened recently that scared the crap out of her when she wasn't crated? Is there something you usually do with her that you don't do when she's crated?

You mentioned she yelps when you try to pull her out by the neck via her collar -- have you taken her to the vet to rule out injury or illness causing the behavior change? Also, that isn't helping, it sounds like you're just hurting her. Force is not helpful.

There's a lot that could be going on here. It sounds like she's retreating to the one place she feels safe and staying there no matter what.