I just bought a heated bird bath to help birds this coming winter.  However, I read a story online about two cardinals' wings freezing up after bathing in a heated bird bath in extreme cold.  The birds had to be thawed out in a kitchen sink before they could be released.  Is this a widespread problem?  Should I put something over the bath to restrict access to only drinking and not bathing in extreme cold?

Thanks!

Mike, a northern Illinois birder