Your kids will need helmets. Ask the instructor if they have helmets that you can borrow and if they can fit the helmets. Helmets are not that expensive (considering you are literally protecting the child's life).
Troxel brand helmets make a wide variety of styles of helmets, and they have some that are not very expensive (the lower end starts at $25 or $30). You should see if you can borrow the video "Every Time, Every Ride" from your local county extension or 4H office. A helmet designed for horseback riding really is best. A bike helmet is not designed to withstand the same stresses of impact in case of a fall. Troxel has sizing charts and additional sizing information on their website at www.troxelhelmets.com. Another brand of helmets are Lexington, I believe, though they are geared more for English (huntseat/dressage) riders.
Check with the instructor, also, regarding appropriate shoes and pants. Most will tell you, especially for the first lessons, that they don't need special riding boots at first, but you do need closed-toed, hard soled shoes, and will need to wear long pants. A t-shirt for the top is fine.
No earrings or jewelry, for safety, and make sure they use unscented soap/lotion/deodorant (and you too, if you're going to be at the barn) -- bugs & bees love scented stuff and are drawn to it.
Sunscreen, if riding outside. :)
I hope the kids love it as much as I did! I rode in a borrowed helmet for 3 years before I got my own helmet (helmets are definitely cheaper now than they were when I was a kid).