JRT puppy pees in crate

First of all thank you very much for responding to my previous question about my scaredycat JRT. I'm having another problem - our 4 month old puppy won't pee outside when we want her too. We have stayed outside with her on her leash for literally an HOUR and she won't pee. We've tried going on 30 minute walks too and it still doesn't work. As soon as she steps foot into the house she'll either pee in her crate (while throwing a tantrum to be let out) or pee on the carpet. I read somewhere that her crate might be too big but it's the size that the breeder sold to us - she can turn around if she has too and her back touches the roof of her crate while she's standing. I'm wondering if the reason she pees inside is because it's really cold outside (going from cold to warm). Pleaase help.