I really enjoyed this story! I love how you said the world of snow outside was her friend, that made me smile. I also liked how the cat's name was Leo. It's a name I have a guilty pleasure of seeing. Thanks for posting this!

Your descriptions are good but you could add a little more tension. If the kitten tries to run and Amy looses sight of it she could go home, get a piece of fish or chicken and lay it down where the animal was. Then after an anxious wait it could return, drawn by the scent of food and this time let Amy take it. A little more difficulty would make a more interesting story.
Its a good choice of subject.
I've got a cat story on page 11 of this site, 'Misty's Cry,' and there are more besides.