It can be done with a mobile if you your OS is Windows Mobile but it does require an addon that allow you to reference your data storage on the phone with a drive letter as the PC does. Since each phone's hardware is different, you'd have to get that addon from your phone's manufacturer. Some manufacturers may not provide it though. I have seen it once from HTC for a PDA.

My advice is avoid the trouble and get yourself a cheapo laptop and either use a mobile internet dongle or link the laptop via your phone for internet access.