OP, don't listen to these jerks. Your phone will work just fine in Canada.
However, that might be your biggest problem. Allow me to explain.
Most cordless phones manufactured nowadays use encryption algorithms to encrypt your telephone conversation between the phone and the cordless receiver-- this is to prevent anyone with a radio scanner from listening in on your phone conversation.
However, the US Government has imposed strict limitations on the export of products which implement advanced encryption methods--I suppose the government fears you must be a terrorist if you have something you want to hide (encrypt). The US actually classifies encryption methods as "munitions", and treats their export just like the export of any other munition (say, a high-powered rocket launcher).
This may sound like a joke, but the FBI and the RCMP (Royal Canadian Mounted Police) have a joint enforcement effort called "Operation Can You Hear Me Now?", where they use special radio scanning technology (similiar to that used by the FCC to find pirate radio stations) to locate devices which emit encrypted voice or data signals. If caught with such a device, you can be extradited and charged with the unlawful export of munitions, a crime punishable by up to 25 years in prison per offence.
My advice, if you still choose to ignore the law and move the phone across the border, is to use the phone as sparingly as possible to minimize your risk of being caught.