Sorry to burst a bubble, but we've had many Oct, Nov, Dec babies - from small Shetland size up to full size riding horse w/o being under lights or in barns/stalls - in snow country MT, in CO and here in NC (remember the filly I just had born the day after Christmas & we purposely bred an Arab mare in November 07 hoping to get a baby close to Oct 1st, 08 for our daughter's Bday. That mare WAS preg maiden and the colt was born Oct 17 and due to circumstances, the daughter he was meant for was the first to find him when she foaled in the pasture after being turned outside for a while, but I was called to a friends' for help with one of their horses).
Most breeding/stud farms that I'm familiar with separate weanlings by sex no later than 6 months because, yes, both can produce (impregnate and get pregnant). I was caught by surprise last week - with everything going on this year, I hadn't paid attention to the fact that our late 2015 colt, Riddler, was 9 months old... Till I caught him with a full erection, mounting a mare in the pasture. The other stallion drove him off at that point and I caught & pulled him out and he's now weaned in a paddock in the boy's pasture. Later today and tomorrow, I plan on turning him out in the boy's paddock for a few hours to play and run, but he will be in the pen at night (for now). He will be about 14 months old when he is scheduled for castration (unless I do it before then - but the vet school likes me to bring these little guys up for their students and I LOVE having no cost castrations, even if it's a different student removing each testicle). Now I also need to keep an eye on his 1/2 sister - Blitzen, the filly born the day after Christmas - as she's now 5 1/2 months old and I wonder... UGH! In the past, we've usually weaned babies between 4-6 months old and then kept the colts separate from the fillies/mares. Next week, I will be pulling Blitzen out of the pasture and weaning her - to make sure that if she does come into season, the mature stallion running with those mares doesn't breed her. I meant to pull that stallion out before the 1st of June, now it will be a bit later...
I really hope for your filly's sake (& your peace of mind) that she isn't in foal, but if she is you have her at a great time to get everything in order and get her in good shape with your care. We are here for help if you need it.
I came from a ranch background that routinely bred 2 yr old fillies. Some of those, due to time of year actually born themselves, were much younger than a "true" 2 yrs old... Even here in NC, there was a Paso farm (can't remember if they were Peruvians or Finos) that bred their 2 yr old fillies first and then trained them under saddle while they were pregnant. They were then trained to ride when their foals arrived - some of those girls seemed soooo small/tiny (under 13 hh - way too small for me to ride!) when I rode along with the vet to do ultrasounds at the farm. How they did things at that farm was fascinating! We ultra sounded 15 fillies one time - I seem to recall several being not pregnant. The farm also used that as a determination on who to sell and/or at what prices... The ones not in foal were biopsied right then to see if something was wrong, then all of the open fillies were sold.
Her hooves will come around to some extent. I know that my farrier would want to do her every two weeks for a while - so that only a little done at a time to prevent her from being too sore and to promote growth.
I look forward to hearing what you've named her - she's a real cutie (& I don't normally like "red" horses).