In Warwick town, or in the castle?
The Kingmaker exhibit is indoors, and that's suitable for all ages (although I remember taking one set of friend's kids there and they were scared by the lifelike mannequins!), there's another indoor bit too, with mannequins etc, which isn't quite as child-friendly. The great hall is obviously indoors. Down by the river, there's the old mill, which is also all indoors.
If you have younger children, there's usually a storytelling thing somewhere (like a Princess tower or some such), and if you have older (braver) ones, there's the dungeon (which you have to pay extra for).
But you're right - lots of it is outdoors. But unless it's chucking it down then you'll be fine with waterproofs.
The castle don't like to let you know that you can come and go (I think you have to get your hand stamped, so don't just leave without checking!) - they want you to stay within their bounds and spend ALL your money with them. But Warwick itself is full of lovely independent business who would dearly love you to visit them! I'd strongly advise lunch outside the castle - so many better options. If you exit the castle through the main town gate, and walk straight up to the main road through town you'll get to my favourite coffee shop - Jack's Shack - where you can get a lovely sandwich and a drink. Or for tea and cake, there's Thomas Oken tea rooms, right outside the castle walls. If you're staying overnight and want dinner recommendations, shout up!
There's a free museum in the main square which could pass a bit of time if it's raining. There aren't lots of other indoor things to do in town, other than look in the shops and eat cake. If you do find yourself spending time in town, there is plenty to see below the East Gate (which looks like the 'end' of town if you're just glancing in that direction).