Real-time information about the friction coefficient between the tyre and the road can be used to improve active safety systems and is an enabler for autonomous vehicles. Large tyre force excitation is normally required to obtain an accurate friction estimate. This paper quantifies this requirement for four different tyre models on wet salted asphalt at water freezing temperatures. Cost functions and different tyre models are evaluated and the results are compared to a previous study performed for snow conditions. The suitability of commonly used tyre models for friction estimation on snow and wet asphalt has thus been investigated.