I'm a guy, but most of the women I know stop riding very early in their pregnancies. There are plenty of teenagers who will keep your horse fit for you, and even compete him if that's your desire.
Having said that: Horses are individuals; whether or not yours takes to driving is anybody's guess. But breaking a horse to drive is just as dangerous as riding; perhaps more so. Then you've got to retrain, once you're ready to get back in the saddle.
Your life is changing. You can keep spending time at the stable, grooming, going for walks in-hand, and socializing. Do the smart thing for you, your future family, and your horse: find someone to keep him in training while you're getting your family started.
Eva, I've been around horses, and horsewomen, for around 40 years. That includes watching little pony girls grow up, start their own families, and get their kids into the saddle. It's been a privilege.
The women I know don't ride while pregnant, and take extra care with groundwork. I'm just reporting my observations of what smart horsewomen do.