i don't know about horse chestnut - but sweet chestnut i use all the time.
for most of the following:
pea sticks and bean sticks
hurdles (gate and woven)
shingles
edges - for borders and raised beds as well as stakes to wedge them in.
post and rail fencing
trellice work
poles for swings and climbing frames - for kids
logs (for wood burner- as the wood spits a bit - but keeps in for ages - so one of the best woods to use in sealed units)
like munty said before - chestnut is a great wood to use - but it will split if not handled properly.
if you have to fix it /something together - pre-drill - or it will split (slowly at first - but the split will run)
it's great because it splits - with a good knife - or wedges (depending on size) you can get just the right shape and size that you want.
if you want to use for post and rail - or something architectural - then it will actually last longer if you remove the bark - this is very easy to go when it's green, but alot more like hard work when dry.
also - the longer you leave it (to season) the hrder it gets - so work it green - use it dry