You are not running windows. There are no known virus or trojans for the PalmOS. The only issue is leaking data along the way to the web site.
For example the EVIL TWIN issue noted at http://reviews.cnet.com/4520-3513_7-5630181-1.html which is something it won't matter what you used.
Bottomline. Don't bank or much else on unsecured wifi locations.
I wonder about security using my Sprint Palm 755p on the internet. It is a terriffic internet tool. G-3, etc., even TV, but it does not have typical security software, and I don't know how safe it is off https sites.