We've only had 3 pregnant mares and I really didn't notice much of a change in their personality during or after there foaling.
I've heard it said too, but in my limited experience I would have to say JDI is right that its an old wives tale.
I'm not sure about all mares, but it worked for one of the TB mares at my barn. After she had her first foal, she was still a little flighty but she was a lot better, and since she was a maiden mare she treated her baby awful. But when she had she second foal, she was a totally different horse. And I'm not saying every maiden mare would treat their baby badly, just unfortunately this mare did.
Also, I think if the sire has strong enough genes that the mare doesn't pass along all of her personality traits. Both fillies that came out of that TB were nothing like their mother personality wise. I've also seen cases though where the mare has a more dominant gene, and the foal is just like the mother and it turned out to be a bad thing.
In my experience and opinion, some mares do "settle down" after having a foal... now, whether that's age-related (as in, the mare's now a year older than when she was bred) or a hormonal thing... anyways, it doesn't hold true for every mare, and in my opinion, it is a mindless reason to breed a mare. People are always trying to correlate things - such as with cell phones and brain tumors... it's been proven untrue... doesn't mean people don't still believe it.
If you're going to breed, do it for the right reasons... as in, the mare's done something in her life, or has accomplished something, or has exceptional conformation that you want to pass on to a foal, etc etc etc (like you can see in my other threads on the topic) .. but making a mare pregnant just to make her settle down? No, that is not an acceptable reason in my mind.
If you want to get a mare to settle down there are some amazing supplements out there that do that. To name a few: - Compose - "Chill" by Omega Alpha - "Feisty Mare" by Herbs for Horses
- "Moody Mare" by Wendels ... even a hormonal replacement from your vet! There are a million other ways to get a mare to settle down than getting her to have a foal... having a foal is expensive and risky.
Talk to your vet... I will almost bet on it he'll say the same thing.