Those devices are typically called
netbooks now, which are generally just small laptops.. the majority of OpenBSD developers use laptops.
http://www.openbsd.org/i386-laptop.html documents some of the available choices, it's selection of "Eee PC's" is rather vauge though..
But really, the first thing one should do is check the mailing lists..
http://marc.info/?t=122151386700001&r=1&w=2
With one of these newer devices, following -CURRENT might be necessary.. this seems to indicate the wired Ethernet may be one of the unsupported Attansic chipsets.
The wireless on the other hand, might work.. with ACPI enabled..
In essence, you may have a little work on your hands.. trying to get everything working as desired.
Have fun.