Cold load pick-up (CLPU) has been a critical concern to utilities. Researchers and industry practitioners have underlined the impact of CLPU on distribution system design and service restoration. The recent large-scale deployment of smart meters has provided the industry with a huge amount of data that is highly granular, both temporally and spatially. In this paper, a data-driven framework is proposed for assessing CLPU demand of residential customers using smart meter data. The proposed framework consists of two interconnected layers: 1) At the feeder level, a nonlinear auto-regression model is applied to estimate the diversified demand during the system restoration and calculate the CLPU demand ratio. 2) At the customer level, Gaussian Mixture Models (GMM) and probabilistic reasoning are used to quantify the CLPU demand increase. The proposed methodology has been verified using real smart meter data and outage cases.Index Terms-Cold load pick-up, distribution systems, service restoration, least squares support vector machine, Gaussian Mixture Model.