In order to describe the behavior of the car under ice and snowfall conditions more realistically,a vehicle following model based on the full velocity difference model is proposed under the premise of considering the speed difference and various kinds of ice and snowfall conditions. Under various road conditions,it obtains the critical stability curve of the model,and verifies that the worse the road condition is,the less stable the traffic flow is. In addition,the method of nonlinear analysis is used to obtain the solution of the kink density wave in the space headway under the unstable region. Finally,the conclusions are verified by numerical simulation,that worse road conditions,which means the road surface friction coefficient is small,will lead to greater instability region and worse anti-interference ability of traffic flow,and even cause more congestion and accidents. The conclusions make great contributions to handling the traffic jams and security issues under ice and snowfall conditions. In order to describe the behavior of the car under ice and snowfall conditions more moreistically, a vehicle following model based on the full velocity difference model is proposed under the premise of considering the speed difference and various kinds of ice and snowfall conditions. Under various road conditions, it obtain the critical stability curve of the model, and verifies that the worse the road condition is, the less stable the traffic flow is. In addition, the method of nonlinear analysis is used to obtain the solution of the kink density wave in the space headway under the unstable region. Finally, the conclusions are verified by numerical simulation, that worse road conditions, which means the road surface friction coefficient is small, will lead to greater instability region and worse anti-interference ability of traffic flow, and even cause more more congestion and accidents. The wise make great contributions to handling the traffic jams and security issues under ice and snowfall conditions.