I used to ride the TB mares at the farm I managed. Just around the paddocks and cattle pasture to check things. I'd even hop on one to go get the mail. Sometimes I'd ride one and pony another to get two of them out and about. I have a boney backside, and when the mares became large enough that my old hunt saddle didn't fit well, I used a bareback pad with extension on the girth.
It's good for them to get out and move, just as it is for pregnant humans. The only downside was they all foaled with incredible ease and the owner never got to witness a foaling in the two seasons that he flew in to "help." Our vet had a place next to us. His wife also rode their pregnant mares and had similar experience.
Our paddocks there weren't large enough to encourage long walks for the mares, so I felt walking and a bit of trotting were beneficial and needed.
But when ranching in WY and MT, until the mares were close to foaling, they were pastured on large spaces. They had to move to graze and then go to water. The layout of the pastures required them to stay in better shape. They, too, always foaled with ease.