For people I would recommend kerrits ice fil breeches, they're lightweight, cooling, & conveniently have a pocket!
I love EIS shirts! They keep you very cool while riding, and they provide protection from the sun!
PS: there are also lots of breeches made to be used during the summer! The materials are lighter and they keep your legs in a good temperature. I have some breeches of a Spanish brand called Lexhis, but I'm sure there are loads from other international brands.
I know some brands which sells products really nice for the summer, like Kastel Denmark and EIS, they have long sleeve shirts which regulates your body temperature and make it colder during the summer and you don't get your arms burned because of the long sleeves. Ariat has a really good quality products which help you to take all the sweat out of your body and some tech materials which helps your body to get colder.
Hope it helps!
High Class Equestrian for the people !
For the horse, I know that there are carpets that are antiperspirant brand HAF (it is a French brand, but their items are very good and very effective). There are also tendon boots that allow the legs of horses to stay cool. For my horse, before making a course when it's hot, I use a sponge that I wet and that I pass on the body of my horse. In order to refresh it just before starting the course.
For the rider, nothing better than equipment for sportsmen, socks / tee-shirts antiperspirant and airy, the same for the pants of riding. The riding cap is also an accessory that must have aeration (because the sun on a black bomb is not great ...). The cap is also important against sunstroke. After the most important is to do small sessions and put yourself in the shade to have freshness. It is also necessary to make a relaxation and recovery long enough not to make an effort too sudden and not to stop suddenly. The horse should be drunk before and after, but he should not drink too much or too quickly.
Have a good day