Puppy that urinates in crate

I recently brought home a JRT puppy. He is 10 weeks old and very intelligent. However, I am having some problems housebreaking him.

I am temporarily living in a sixth floor apartment (awaiting the refubishment of my house, which has a big fenced in yard for the little guy!). So I am paper (and crate ) training him for now. He has started to catch on, but still often runs INTO his crate to pee, instead of on the paper.

He was raised at a horse barn and was kept in a horse stall with his littermates. As such, I think that he learned to eliminate where he sleeps. I am not a novice at housebreaking or crate-training, but have never run into the problem of a puppy that prefers peeing where he sleeps!

I was wondering if he might grow out of this habit as he gets older.

Also --- I 've tried taking him outside to go --- have spent HOURS with him patiently waiting ---- but he will only 'go' at the barn where he was raised! If I walk him anywhere else, he will 'hold it' until he gets back to the apartment, or into his crate.