The Witch's house appears to made of Gingerbread. You can eat the roof and sides, but not the candy canes or gingerbread children. You can enter the house safely as long as the witch is not home—she doesn't take kindly to visitors. To tell weather or not the Witch is home, try and eat some of her house. If you hear a voice from inside, you know she is home. If not, you're free to rob and pillage the nasty old hag.
There are two items of interest in the Witch's house, some cheese located in the cupboard and a note on the end table by the Witch's bed. It is probably best to first deal with the Witch before gathering these items as if she happens to come home with you in the main room, you will be captured and turned into one of the gingerbread children.
Dealing with the Witch is easy. Go into her bedroom and stay behind the wall until she comes into the house. She will begin talking to herself about who she is going to eat for dinner while she strews her cauldron. While she is busy with that, you can sneak up behind her and give her a shove into the pot. She will quickly melt away and be no more bother during the game.
There are two Easter eggs in the Witch's house: First, while standing in front of the cauldron, look at the smoke rising up from it several times. Sometimes, an evil face will appear in it. The second Easter egg can be found by looking at the note from the end table several times. On occasion, it will say something different.