The development and aftermath of a snowball Earth during Precambrian time still raise questions, particularly the process involved in the deposition of the associated cap carbonates and the time required for the Earth to return to more stable and less extreme climatic conditions. We present numerical simulations modeling the chemical weathering of regolith exposed to a CO2-rich atmosphere after deglaciation. We consider the effects of an early cation-proton exchange reaction that promotes fast initial dissolution of the regolith, a reaction often omitted in the modeling approach but one that becomes particularly important under acidic conditions and in environments where glacial erosion can substantially refresh the rock surfaces. Calculations show that this dissolution step may contribute significantly to the riverine ionic input and may promote the deposition of thick cap carbonates over a short period of time. The long-term weathering of the regolith becomes predominant, representing an efficient way of removing atmospheric CO2 over periods ranging from tens to hundreds of thousands of years, depending on the grain size of the regolith material.