Hey look, there was a grey horse under there!
She should shed out fine. Emaciated horses grow "starvation coats" to protect their bodies. My filly (sold now) had a coat just like you're mare's is, and while it took longer for it to shed than the other horses, she did shed and had a decent summer coat by early May. This year her winter coat was normal thickness.
(terrible edit- sorry. General idea of how thin and hairy she was...but horses that weren't mine were in the background)
After finally shedding out in May (and growing a LOT)
then this winter - totally normal hair growth.
If you clip and blanket your mare, with as thin as she is, I would think there would be a very big chance of her getting sores. She has no muscle or fat so the blanket would be directly rubbing her bones. Ouch! If you must clip, do a bib or low-trace. I think she'll be fine though personally. I'd actually be afraid of cutting her when clipping at this point.