5'1" is not THAT short for a woman, it's only about 2 inches below the global average. I would think you would be able to find some from any reputable brand in women's size. 'The North Face' comes to mind. They're great quality and specialize in cold weather gear.

https://www.thenorthface.com/en-us/womens/womens-bottoms/womens-snow-pants-c213401/womens-freedom-insulated-pants-pNF0A5ACY?color=JK3&length=REG

When it comes to height, if she is a little heavier, you want a larger waist size with a shorter leg inseam.