Nice work! The pixel art is cute and the sound effects fit well :)
Initially I did not understand what I was supposed to do when Grandma asked for wood, since I had just been seeing lots of wood and burning them, and going back to the unburnt ones gave no way to fetch it. It's only after reading comments here that I knew I could go further somehow and tried again.
I agree with others that allowing Enter to dismiss dialogs would be nice, so that we don't need the mouse at all.