Ok, so you know how it's common for first time mom's (human) to have a longer gestation, but additional pregnancies can have a shorter gestation . . . is this true for broodmare's also? 

They can be different each year.  I track my broodmares, here is an example:

Every time is different. Every mare is different every year.

BUT - generally, mares carry a little longer as the years go by.

My observance is that mares due early carry longer and in May-June carry shorter. But I'd have to get my book out and put together a nice spreadsheet like WB.

I'm jealous of WB tho -- my mares always keep me waiting waaayyyy past 340 due dates!!

Have you noticed a difference between colts or fillies??

all fillies except 2018

Our mares are very consistent, but we don't breed a ton of foals either.

Mare 1: 5 foals, all between 319 & 321 days (9 years between first & last foals. 4 fillies, 1 colt.)

Mare 2: 2 foals, 345 & 346 days (7 years between foals, both colts.)

Mare 3: 2 foals, 359 & 356 days (3 years between foals, both colts.)

Mare 4: 3 foals, 334, 334, & 335 days (6 years between first & third foals, 2 colts & 1 filly.)

Mares 2, 3, & 4 were all daughters of Mare 1, and 3 & 4 are full sisters. Interesting how even closely related mares can have such different gestations!

Ok so her prior  gestation dates are ~338 and 339 days with 2 years separating those. Hmmm

I try not to expect any of my mares to do the same thing every year.  I track them all starting before 300 days and watch them closer the more signs I see. I do have some mares that tend to go longer or shorter. Sex of the foal doesn't seem to make a difference.   

We've noticed that in our area this year, a lot of mares are holding on to their foals longer and the gestation lengths are shooting any averages out of the water. We had a really late winter (huge storms in February, like most other places), so I'm wondering if that has something to do with it- the mares' internal clocks are slightly behind, for example.

I think it depends on the mare.  I've owned two mares that foal on the same day of gestation each time. And others who do whatever they want LOL. 

One foaled at 343 the three times I bred her.

The other foaled at 352 the three times I bred her. 

I think some mares are very consistent, regardless of gender

Some are consistent but vary if carrying a colt or a filly

Some are random..