Make sure that the foal sucks. A normal foal should stand and drink from the mare within two hours. If the foal is having difficulty sucking, or is not interested, he may have serious problems. Call an experienced horse vet sooner rather than later.
Colostrum, the first milk, is very important. It contains all the antibodies your foal needs to protect him from infectious disease. A foal needs between 1.5 - 2 litres of good quality colostrum. It is most important to make sure he gets enough.
If the foal won't suck you can collect some colostrum from the mare and give it by bottle. Or the vet can put it directly into the foal's stomach using a tube. Colostrum substitutes are available if the mare doesn't have any milk.
The foal's intestines can only absorb colostrum for the first 24 hours or so. After that, the vet can give a plasma transfusion to boost the antibodies if necessary.
Check that the foal is passing meconium. Meconium is the firm dark feces that has built up during the foal's time inside the mare. Colt foals, in particular, can have problems passing this because their pelvis is narrow. Your vet may recommend giving an enema.
It is a good idea to have the vet to give the foal a check-up. The vet can give an injection to protect the foal from tetanus. This is especially important if the mare has not been vaccinated recently. A blood sample can be taken from the foal to check that adequate antibodies have been absorbed.
Probiotics may be useful in preventing "foal heat scours", which often occur about 10 days of age. The diarrhoea is probably due to the digestive system adapting to life outside the mare rather than anything to do with the mare's hormones.
Carefully monitor the foal's progress. Even those foals that appear normal at birth can develop problems later on. Foals should become brighter and more active over the first few days. One of the first signs of serious infection is that the foal becomes dull or spends more time sleeping.
With good care and attention from an early age you and your new foal can look forward to an exciting future together.