you definitely need a deep, full bed on top of the mats, and leave it deep litter until foal is a week or so old at least. as wally says, rubber is slippery. straw is traditional in case the foal inhales or swallows shavings, but with smaller ponies, the straw can be very hard for the newborn to walk in or get up in, as it tangles round their legs. we use shavings and our vets are happy wit that - we disinfect and deep litter it (about 8-12 inches of bed) with clean shavings a week or so before baby is due, and only mum goes in there so it has her 'bugs' and only her bugs, as baby has no immune system at first, but will be used to mum's. we deep litter so it forms a solid base, easier for baby to get up and down on.
we have them in for foaling because it's easier to watch, and easier and more accessible for the vet if needed, and lights are there. in the worst case scenario of a 3am foaling on a dark night that needs assistance, it's easier for the vet to help if they're accessible and somewhere with lights. they go out in the daytime, in a paddock with chicken wire round the bottom half of the fence so that if she foals in the day, she can't pop baby out on the other side of the fence!