Renault Clio I Petrol d type engine - engine misfires when cold - chub

Hi bought my daughter a nice little car to learn in ,one owner 60,000miles flew through mot .It starts 1st time uses no oil or water and there are no warning lights on. I serviced it new oil, filters and plugs ,during the summer months it ran great apart from a slight hesitation when accelerating, once you reached your speed it ran fine .In the last two weeks now the weather has gone cold it misses and f***s and tickover is up and down and pops.After about 10 miles it runs fine. Any help would be appreciated !