How scary Mary! I am sure you had your heart in your throat! How long did it take for your vet to arrive to get that baby out? I am just curious so that I learn from everyones experiences. I am going to mention the tube down the windpipe deal to my vet. She is just a beautiful Easter present! Congratulations to you!!
For one that is slow to find the milk bar, we bottle fed our newborn Quarter horse filly 3 ounces of milked colostrum. Then she took a nice long nap and when she got up I held the mare and my husband cradled the filly guiding her head towards the udder and got her trying to suck his finger then got her to the nipple. Once she tasted that same taste she got in the bottle, she was a quick study. This was a suggestion from my vet. The main thing was getting her fill and then a nice long nap and then she would be hungry again and have the strength and the taste.
Also, not to be negative, but you may want to check her palate to rule out a cleft palate since the milk came out of her nose. I agree with what the other said though, that it more than likely was a full udder that let down and was just too much for her to gulp down.