bittrex support BTG. the future There must be a lot of wallets that support BTG. In addition there are many sites that can deposit BTG
It does not support it as a matter of fact they say they don't trust it but they will give to anyone that wants it. They are NOT listing it.
Actually they not fully support bitcoin gold as the statesment they just efforts to credited BTG to all user on Bittrex who have bitcoin in their account. And does not guarantee BTG will be listed there
If Bittrex exchange support user receive Bitcoin Gold, it means Bittrex also accept Bitcoin Gold and will list it on their exchange. There are many exchanges do not guarantee list Bitcoin Cash in past time, but after support user receive Bitcoin Cash, these exchanges also listed this coin (Poloniex, Bittrex).