First, look at the neck. Mares become pregnant and the neck contracts a bit. When fillies become pregnant (a rare occurrence) the neck becomes wider but not thicker.
As the pregnancy continues, look toward the abdomen. The colt will expand her midline and make it difficult to set a girth strap -- which means you don't saddle her again until four months after she drops her colt. Never set a girth strap tight on a mare anyway.
Next look at the nipples and teats. Horses don't have the udders you see on cows but they do produce milk. When you see milk, the mare is about to deliver. Put her in the stable, extra grain and hay, and maybe sugared water to get her that extra little bit of energy to deliver a healthy foal.
Once your mare delivers, celebrate and walk her around the stall just to make sure she doesn't lay down. Keep that going for 24 hours and make sure your mare and foal get plenty of care. Keep the mare and foal together for about 12-14 weeks, then wean the colt.
Pretty soon, you find another horse in your herd. That is all the better!
How interesting, My grampa raised quarter horses. I grew up with horses, but I never knew that about the neck.