Yes, this one is perfect.
As someone else suggested, you want to get a long one. One that covers the butt, at least.
That first jacket won't do in NYC, either. We still get the wind child down to 10 degrees.
Yes, that one is fine, too. Always get a DOWN jacket. Get a half - to whole size larger. A winter coat should not be snug. She needs room to be able to layer clothes underneath, and there should be some movement & air inside for insulation. Her own body heat heating the air inside will be what keeps her warm. Notice down jackets are
puffy. That's the insulating air in the jacket. If she has an insulating layer of air between her clothes & the jacket and another insulating layer of air IN the jacket, she should be fine.
And, as others have mentioned, if she is far upstate, the wind chill makes a big difference. If she's near Rochester/Buffalo, the wind whipping off the Great Lakes is brutal. I haven't been up near Potsdam, and I have no intention of being up there in winter.

I'm originally from the mid-region and I been through blizzards. While it is not as cold down here, I HATE to be cold.
Get plenty of thermal under shirts & pants. Also get boots a half size larger, so she can wear an extra pair of socks if necessary.