Off the top of my head (so I might miss something)
My kit has:
Bottle of pre diluted vetadine for washing hands
Bottle of vet lube in case I have to go in
Can of cetrigen for spraying the stump
Heavy duty peg for clamping the cord if I need to cut
Scissors for cutting (ALWAYS clean and always sprayed with cetrigen just in case)
Sharp clean knife in case I can't tear the bag
Many towels for wrapping the placenta and rubbing baby down if needed (didn't bother this year and left it to the mum's)
Extra torches
Up in the shed I have foal rugs, more towels, painkillers, wormer. I have a stable ready, or all the stuff needed to make it ready on hand. Next season I'm hooking my phone up to a bluetooth so I don't need a hand free to call for help.
Clothing wise I mostly wear singlets and a vest, only one jacket with sleeves and it isn't zipped up. I can strip very quickly to go in if I have to!