According to Obtain client MAC address in ASP.NET Application, it is not possible. I am not entirely convinced because whenever I connect to Tim Hortons WiFi, my MAC address is known.
Occasionally, the network is slow and I see this URL like this before being redirected to the Connect page:
http://timhortonswifi.com/cp/tdl3/index.asp
?cmd=login
&switchip=172.30.129.73
&mac=60:6c:66:17:1a:83
&ip=10.40.66.229
&essid=Tim%20Hortons%20WiFi
&apname=TDL-ON-NEP-02177-WAP1
&apgroup=02177
&url=http%3A%2F%2Fweather%2Egc%2Eca%2Fcity%2Fpages%2Fon-72_metric_e%2Ehtml
So according to this URL, the site knows the IP address of the router, my MAC address, the IP address assigned to my device by the router, the network SSID, some other pieces of information, and the URL I was trying to access prior to connecting.
There's two options: Tim Hortons WiFi Basic and Tim Hortons WiFi Plus, where the "Plus" option allows me to connect to any Tim Hortons WiFi access point in Canada automatically with this device. Registration requires an email address, so I'm assuming this is possible by checking the MAC address and storing it in a database that routers ping upon connection. More info here.
According to the extension of this page, I can safely assume it is ASP. How are they obtaining this information?