I was wondering is there such thing as an offline wallet for our smart phones? There are a lot for pc but I haven't heard any yet if there is.
My advice is to simply not use a phone as offline storage for any serious amounts of BTC.
You should do that at home and keep it safe, and not carry it around. Use smartphone for change money that you can use to spend, just like an actual physical wallet with some dollar bills and coins.
An old phone that stays offline (hence cold) is perfectly fine for that. IIRC bither does not allow outside connections if its in cold mode.