If you mean your root password "alpine" ... don't !
I don't see why not, just do not forget it. Seriously, do not forget it. Changing the default passwords for either root or mobile doesn't seem to have any affect on any apps or installations.
Changing default passwords for anything is important, this is especially pertinent in my mind with a jailbroken iPhone as having default passwords and apps like openSSH, sftp and wi-fi, if you don't have your phone totally secured anyone could log onto your iPhone and wreck some havoc.
Default passwords + the ability to remotely access a phone = trouble waiting to happen.
Of course making sure you have things like openSSH disabled when not in use is always good practice as well, but say if you forget to disable openSSH and log onto someones network, it would be a piece of cake for a person who has access to the router you are connected with, to get into your iPhone if you leave the default passwords intact.
Lets not even get started on how many default passwords are left on routers. Say you connect to a local pub's free wifi, someone else who is sitting there logs onto the router, grabs all the assigned ips and mac addresses, does a few quick scans, and if you have some open ports or services on your iPhone, combined with the default passwords, well lets just say no good can come of that.
As to the genetics original question about changing a password with winscp, that is a SFTP/FTP/SCP client for windows yes? I'm not aware off hand of a way to change your iPhones passwords with that app. I would suggest getting an SSH client like PuTTY, connect to the iPhone and use the 'passwd' command to change whatever passwords for whatever accounts you like.