No hydrogen peroxide, iodine, spray on wound dressings --all of these products are harmful to the tissues and slow healing. Hydrogen peroxide is far from a good antibacterial cleaning agent too. (information presented at the 2006 AAEP convention)
I would also ensure that the vet's phone number is included in the first aid kit so you don't have to go digging for it in an emergency and a copy of a good equine first aid manual.
Here is are a couple of good links on first aid and when to call the vet, but be warned there are some graphic photos:
I think bag balm is the most essential ingredient for a vet kit.
Bag balm serves as:
A moisturizer for anything very dry
An anti bacterial wound cleaner
Great for rashes stings, bites
Soothes things well. [injurys etc]
A sunburn or any other kind of burn
And SO MANY OTHER THINGS!