From what I've read in the articles I linked above, plus many others, it depends on the network security employed by the hotel. It appears that the majority of hotels do not do enough to secure their networks, whether wired or wireless.
That being said, at least with a wired connection you may be somewhat protected from joe shmoe logging onto the hotel network while sitting in the lobby or in the coffee shop next door. Of course, if the hotel offers both wireless and wired connections, and they both connect to the same network, that all goes out the window.
Again, it appears that a wireless-to-wireless device using WPA2 password protection will allow you to log on multiple devices onto your own network, after logging onto the hotel network with the first device. ASUS claims that their travel routers provide enhanced security in this situation.
As ackattacker wrote above, you still should employ some type of VPN security. Investigate it for yourself - there's a lot of info out there on travel internet security usage.