What is the lower temperature limit for ion channels function?
The lower temperature limit of ion channels likely is dependent on various factors, including the type of channel and the recording conditions (tissue type, medium etc.). Reports on the suppression of voltage spikes (i.e., the inhibition of action potential firing) range from 1 to -20oC in squid axons, dependent on the species (Leuchtag, 2008). I couldn't find information on specific channels.

Reference
- Leuchtag, Voltage-Sensitive Ion Channels: Biophysics of Molecular Excitability (2008)