Hi Kami!
I would absolutely recommend packing the snacks your children enjoy if at all possible. It's possible that you might not be able to find a particular brand or variety of snack while on vacation, and if your children have favorites you will want to make sure you have those on hand. Prices for most items are fairly reasonable, but the sometimes the selection isn't always the best.
Another option would be to ship yourself a package from home filled with items that you will need during your stay. Your resort will keep the package for you until you check-in, and this is a good way to avoid the risk of overweight luggage at the airport!
To ship yourself a box you will want to address it like this example:
Disney's Polynesian Resort
Please Hold For Guest: Amber V.
Checking in: 9/1/09
1600 Seven Seas Drive
Lake Buena Vista, FL 32830
I suggest shipping your package via FEDEX or UPS so that you can track its progress until delivery. Try to ship it with enough time so that it arrives a day or two before you. When you arrive at your resort let the cast member at the desk know that you have a package waiting, and they will be able to assist you.
Finally, there are grocery delivery services available like
www.gardengrocer.com. You can place an order online and have it delivered to your resort so that you don't have to worry about shopping or shipping items from home. Garden Grocer has a wide variety of items available so you may be able to find everything you need for your children on their website.
I hope this helps! Have a wonderful vacation!