Have no cold water downstairs but upstairs is fine its -5 here in ireland

Over here in the USA when the temps get below zero F or 32 degrees F I keep the cold water tap turned on to a slow trickle. This keeps the water flowing as water that is moving cannot freeze. You should be able to have the cold water downstairs flow if you have cold water up stairs. I keep the kitchen cold water faucet turned on when temps are very cold outside.

"water that is moving cannot freeze." moving water is more difficult to freeze but it can still freeze. I think you meant that flowing water has less time to sit in the pipe and dropo down to a freezing temp. Anyway, lets narrow this down. Upstairs you have hot and cold, right? Downstairs you have hot but no cold, right? How many cold water fixtures are affected