Both these trees are from temperate climates and need a dormancy period which is brought on by decreasing day length and, sometimes, colder temperatures. American chestnuts have been subject to a fatal blight for many years so the European varieties such as the horsechestnut are more suitable. As @Grady Player notes chestnuts are big trees with mature heights up to 25 meters:
Horse chestnut has leaves that can approach 1m across and has long internodes so it is very difficult to produce anything that works well as a bonsai.
Hazelnuts or Corylus are a better subject for growing indoors as a bonsai as they will tolerate a small pot size with reduction in foliage size and have an interesting flower called a catkin.
- both are difficult to grow as full size trees indoors without a tall climate controlled greenhouse
- Hazelnuts can be grown as bonsai but will still need a dormant period in the winter.
- neither are suitable for nut production indoors
Here's how to grow a hazelnut from seed
- Collect nuts from the trees rather than from the ground when they begin to turn brown.
- Use the flotation test to see if the seed is viable.
- Hazelnut seeds have a hard seed coat, internal dormancy and irregular germination with increasing length of storage. To overcome this dormancy, the following procedure is followed for C. avellana in Oregon.
- Half-brown nuts are harvested in August and are refrigerated.
- In late November, the nuts are soaked for two to four days in water then stratified in moist vermiculite at 4 degrees C for three to five months.
- After three months the seeds are warmed for 5 days and those with visible root tips are planted in flats in the greenhouse.
- Ungerminated seeds receive further stratification. Seedlings are transplanted after they reach 25 cm.
And to propagate a chestnut or horse chestnut:
- Obtain healthy chestnuts in the fall from a surviving mature tree over 10 years old.
- Store them in slightly damp peat moss, place them in the refrigerator and plant them in March or April. Germination rates often exceed ninety percent.
- Choose a location with full sunlight and slightly dry, well-drained soil.