I have always taken this to be a tactful excuse to allow her to baby-sit Mr Woodhouse and let Emma get out into the gardens at Donwell, without making it obvious to everyone that this is her reason. Mr Woodhouse himself, in his reflections on the visit in Chapter 42, plans to "sit still with Mrs. Weston, while the dear girls walked about the gardens". He is of course oblivious to the possibility that it might not be Mrs Weston's first choice to sit in a room with a fire, on a hot day, with someone who is, putting it as kindly as possible, not a scintillating companion. After some hours of it, relieved only by a short walk (in the highest part of the gardens, which not even Mr Woodhouse could imagine to be damp) and a meal, Emma takes over Woodhouse-watch to allow Mrs. Weston to be "persuaded away by her husband to the exercise and variety which her spirits seemed to need".
Furthermore, surely only the Woodhouse party ever planned to come by carriage, no doubt for Mr Woodhouse's sake. Mr Knightley specifically says when proposing the party that it can be done without horses, though Mrs Elton plans for donkeys.