During a campaign, an officer was generally allowed a small Wagon to carry personal effects and anything necessary for his work in the field. This would range from a tent and necessary notes to liquor and personal reading. Naturally the higher the rank the more you'd be able to have bit the more you'll also need for your own command (maps, rosters, etc).

The main people to have a Wagon would be chief De batalion whom commanded a battalion (the smallest unit of independent command) on up. High ranking commanders would get a larger baggage train as they'd be allowed more personal effects and need more things relevant to their command.

However one thjng that officers were not allowed to have was wives. While this wasn't allowed, this didn't mean that it did not happen. Generally wives never accompanied commanders, commanders would take mistresses (such as Marshals Soult and Massena during their command of the Pininsular campaign).

As for horses, generally officers would be on horseback while moving but leading from the front (if that was their choice as not all commanders were the ideal leaders like Lannes or Oudinot) on foot. The reason of not being on horse has more to do with being a larger target for sharpshooters and the chance of having a horse (expensive for a lower ranking officer) dying and even falling on you if you're on it when it dies.

I hoped this helped, for more information on the organization of the French Army I'd recommend looking at Swords Around A Throne by John Elting, a very accessable and cheap book.