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It depends on how cold it is. The phone is not designed to work below -10°C or above +45°C.
If the temperature is not below -10°C, I suggest that you perform a software repair via SUS:
www.sonymobile.com/global-en/tools/update-service/
Should the problem still persist, you can contact your local support team to get information about nearest service center so a technician can examine your unit:
http://www.sonymobile.com/global-en/support/contact-us/contact-info/
I have the same problem, how can I fix it? I can't use my phone outside (and sometimes inside) unless I restart it but it work only for some seconds in cold weather, the cold weather I mean is about 0 degree centigrade.
I have the same issue. Everything is fine and working. But if I leave the phone overnight in my cold bedroom (~5°C) the touchscreen stops working.
After the phone being in a warm room for a while a reboot solves the issue.