I'm seeing some misinformation in this thread. Even if you connect via WiFi, hotels are still able to match a particular web-browsing session to a name/room because they ask you for this information after you connect to their wireless network, usually in a form that prompts you when your browser first opens. All web-traffic you generate in your room will go through the hotel's router, which then forwards your packets to their intended destination by looking inside the packet header for the destination IP address. If the hotel was motivated enough to obtain the IP address of the web server on which this forum operates, they could easily create a rule on the router that flags all incoming and outgoing traffic associated with it. This would pin a particular browsing session with this forum to a room/user. This all may sound complicated but in reality creating a router rule like this is effortless. The harder part would be integrating this information with the players card system.
So now, if you're using a players card, they would know that you frequent this site the instant they run your number.
I'm fairly certain that logging internet traffic on a network that you own is
not illegal because they are responsible for any traffic on it - meaning if some idiot downloads copious amounts of copyrighted material or conducts other illegal activity, the hotel would be held liable for it. I've seen cases where people have been hauled off to jail because they forgot to secure their wireless internet at their house and someone on the street downloaded illegal content. Also, ISPs keep logs of your browsing constantly (and the gov't even encourages them to do so).
To avoid all of this nonsense, simply browse using a proxy server while you're in your hotel room. This will mask your web-browsing at the cost of a bit of speed. Here's a free one:
http://anonymouse.org/.