In winter months when they start to drink less, we add salt to their feed. About a tablespoon right on top, you can buy it in 50lb bags. Makes them thirsty for a drink when they are done eating, and makes sure they get enough water in them to help push all that hay through during the day, you don't want an impaction.
Other than that, everyone else gave pretty much the same advise I'd give. I grew up in Hernando Co. FL before moving to Texas, grass there is a joke, always had to feed lots of hay!!!
oh, and TB's tend to have ulcers, some of them stress easily. Watch to see how much food she is actually eating. If she's not eating the amount you gave her and the other horse is finishing it for her it could be a sign of an ulcer. We had a young TB a 4-H kid got straight off the track and he was getting normal amounts (for a TB
) of hay and grain, but the food would last all day and some would still be there at dinner time. The poor child only had the TB for a week, and I found him dead one morning when I went out to feed. The vet did a necropsy and found that half his stomach was ulcerated and perforated though. He was of healthy weight and was in a paddock by himself because he was new. We noticed that he didn't finish his food, but didn't have long enough to discuss it with the vet before the ulcer killed him.
You're mare is much older, but it's still possible that she may have developed an ulcer recently. Just food for thought.