Is there any need to store gold in chests in my home(s)? Can I be pickpocketed by NPCs in the game or otherwise unexpectedly lose gold or items from my inventory? Or can I safely carry all my gold around?
It is safe to carry around all your gold, even
stolen pickpocked gold, gold stolen off tables and coin purses: Gold is considered to be untraceable, and thus is not confiscated when you goto jail, according to The UESP wiki, and supported by the fact that gold doesn't gain a stolen caption in your inventory most of the time.
However, if you acquire gold with the stolen tag through currently unknown means, this gold will be confiscated when you go to jail, and should be stored in your house.
If you're arrested with stolen gold, it will be confiscated along with any other stolen items in your possession.
Other than that, it is perfectly safe to carry gold around.
Edit: Doesn't match the UESP Wiki, however this is correct. See the comments. Confirmed that my gold is marked as stolen in game, and that stolen gold will be confiscated.