My APHA mare (when she was born) had to nurse like that the first 24 hours, 358 day gestation, large filly = bruised mare, so she was laying down, but filly was determined, and she nursed momma laying down, she didn't care. Since she was a bit over-cooked, she came out ready to eat grain, and was eating a good sized serving of foal feed in a creep feeder at 4 days old.
Almost forgot, congrats on two lovely foals