As far as personality goes, and temperament, it all depends on how they are raised. Set boundaries, teach them their manners, and don't be easy on them just because of their situation. They need leadership just like any "normal" foal.
Also, for a nurse mare foal, I would recommend putting them in with an older gelding or mare when they are strong enough (and healthy enough) to handle that sort of contact. It is good for them to have a "surrogate mommy" of sorts. Of course, you have to take care that the adult doesn't hurt the baby, but if it works out well, it is very beneficial for the foal since they have a role model of sorts to teach them the ropes, similar to what their mother would do.
I have heard it to be a rewarding experience, but don't make the mistake of spoiling the baby because they lost their mommy. They don't know any different and don't understand their plight. They will take advantage just like any other horse would.
Also, be prepared for some rocky roads. It is hard on a foal to not nurse their mommy, and although the milk replacers are very good, they are not always effective and can cause some issues with the foals. Expect some medical problems, lots of vet costs, and some unexpected dips in the road. If you do manage to get along without those issues, then it would be a great surprise, but be ready for a LOT of investment and time. Foals need to be fed often when they are that young, and that means a lot of sleepless nights for you.