Fortunately I have never used poloniex or bittrex, I use a local site that exists in my country, until now there has been no problem.
I think each country has its own site in the case of online wallets, why don`t you try to use it? ...
no not every country has a wallet site , also poloniex and bittrex aren't wallets they are exchanges where you can trade
some people do store their coins in these sites -which is a big mistake - but that doesn't make them wallets , last acts should make people more aware regarding this matter
if you haven't tried them before be cautious when you want to do that , and remember to never keep your coins there