Yes lots of variables but as PPs mention there are lots of things to learn even while walking. I would teach various things like ‘points of the horse’ (which body parts are which), quizzes about horse care, feed, bedding, horse breeds, colours, first aid. Learning theory about riding, dressage, jumping etc. That sort of thing. Also doing fun exercises like touching toes, reaching towards the horse’s ears, ‘all around the world’ where the rider rotates around the saddle, learning the jumping position.
Lots of kids loved these types of lessons, even the more experienced ones and many adults too! It can be really confidence building as well, just being relaxed with the pony/ horse, building up feel and rapport with the horse, not always pushing on, and a good chance to ask questions, also talk about if they feel worried about speed or falling etc and work on that. Some children just like to have a walk and a chat and aren’t horse obsessed or very ambitious so it could be difficult sometimes to get them to do as much as their parents expected them to be doing! But there are always ways to give value for money and for the child to learn. (Aw, reminds me how much I miss teaching!)
It makes sense though for an instructor to mention that the lesson will be more theory based due to the heat because as you say it might not be obvious that there is still a lot of learning happening.
I also remember that lots of parents didn’t want lessons cancelled so they could just have a break for a while! The riding school would be reluctant to cancel because they need the income, regardless of weather.
What does your daughter say they got up to? I would expect a good instructor to be covering lots of the things mentioned above and to give feedback. I would be unimpressed if they just trolled around without enough interaction.