Q:

Why I can not trade coins stored in cold wallet? 

There are two kinds of wallet hot wallet and a cold wallet.  Ideally, people keep minimum balance for trading in a hot wallet and most of the coins are stored in cold wallet.  I am wondering why coins in the cold wallet are not tradable? 

A:

The very point of a cold wallet is that it's less easily-accessible to provide additional security guarantees.  By storing and interacting with your private keys offline, there is a smaller attack surface for bad actors trying to gain access to your private keys.  By removing that friction, you're making that cold wallet a hot wallet by definition.